rhoa.indicators module
- class indicators[source]
Bases:
object- sma(window_size=20, min_periods=None, center=False, **kwargs)[source]
Calculate the Simple Moving Average (SMA) over a specified window.
The SMA is a commonly used technical indicator in financial and time series analysis that calculates the arithmetic mean of prices over a defined number of periods. It smooths out price data to identify trends by reducing noise from short-term fluctuations.
- Parameters:
window_size (int, default 20) – The size of the moving window, representing the number of periods over which to calculate the average.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to window_size.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated SMA values with the same index as the input series.
- Return type:
See also
ewmaExponential Weighted Moving Average for trend analysis
bollinger_bandsUses SMA as the middle band
macdUses exponential moving averages
Notes
The Simple Moving Average is calculated as:
\[SMA_t = \frac{1}{n} \sum_{i=0}^{n-1} P_{t-i}\]where \(P_t\) is the price at time t and n is the window_size.
The first window_size - 1 values will be NaN unless min_periods is set to a lower value. SMA gives equal weight to all values in the window, which can make it slower to respond to recent price changes compared to exponential moving averages.
SMA is commonly used for: - Identifying support and resistance levels - Generating crossover trading signals (e.g., golden cross, death cross) - Smoothing price data for trend identification
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.sma(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 20-period Simple Moving Average:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106]) >>> sma = prices.rhoa.indicators.sma(window_size=5) >>> print(sma.iloc[4]) # First valid SMA value 102.2
Generate trading signals using SMA crossover:
>>> prices = pd.Series([100, 102, 104, 106, 108, 107, 105, 103, 101]) >>> sma_short = prices.rhoa.indicators.sma(window_size=3) >>> sma_long = prices.rhoa.indicators.sma(window_size=5) >>> buy_signal = (sma_short > sma_long) & (sma_short.shift(1) <= sma_long.shift(1))
- ewma(window_size=20, adjust=False, min_periods=None, **kwargs)[source]
Calculate the Exponential Weighted Moving Average (EWMA) of the series.
The EWMA is a type of infinite impulse response filter that applies weighting factors which decrease exponentially. Unlike simple moving averages, EWMA gives more weight to recent observations, making it more responsive to recent price changes while still providing smoothing.
- Parameters:
window_size (int, default 20) – The span of the exponential moving average. Determines the level of smoothing, where larger values result in smoother trends and slower responsiveness to changes in the data.
adjust (bool, default False) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights to account for the imbalance in the beginning periods.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the calculated EWMA values with the same index as the input series.
- Return type:
See also
Notes
The Exponential Weighted Moving Average is calculated using:
\[EWMA_t = \alpha \cdot P_t + (1 - \alpha) \cdot EWMA_{t-1}\]where \(\alpha = \frac{2}{span + 1}\) and span is the window_size.
Key characteristics: - More weight to recent prices: reacts faster to recent changes - Smoother than price but more responsive than SMA - All historical data has some influence (infinite impulse response) - No lookback period required (unlike SMA)
The adjust parameter affects the calculation in the initial periods: - adjust=True: Uses normalized weights (standard EWMA definition) - adjust=False: Uses recursive formula (more common in trading)
EWMA is commonly used for: - Trend identification and confirmation - Support and resistance levels that adapt to volatility - Component of MACD and other composite indicators
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewma(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 20-period Exponential Weighted Moving Average:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106, 108]) >>> ewma = prices.rhoa.indicators.ewma(window_size=5) >>> print(f"Latest EWMA: {ewma.iloc[-1]:.2f}") Latest EWMA: 105.45
Compare EWMA with different window sizes:
>>> ewma_fast = prices.rhoa.indicators.ewma(window_size=5) >>> ewma_slow = prices.rhoa.indicators.ewma(window_size=20) >>> crossover = (ewma_fast > ewma_slow) & (ewma_fast.shift(1) <= ewma_slow.shift(1))
- ewmv(window_size=20, adjust=True, min_periods=None, **kwargs)[source]
Calculate the exponentially weighted moving variance (EWMV) of a series.
This method computes the variance of a series by applying exponential weighting to give more importance to recent observations. EWMV is useful for measuring volatility that adapts more quickly to recent price changes compared to standard rolling variance.
- Parameters:
window_size (int, default 20) – The span of the exponential window. Determines the level of smoothing applied to the variance calculation. Larger values result in smoother variance estimates.
adjust (bool, default True) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the exponentially weighted moving variance values with the same index as the input series.
- Return type:
See also
ewmstdExponential Weighted Moving Standard Deviation
ewmaExponential Weighted Moving Average
bollinger_bandsUses standard deviation for band calculation
Notes
The exponentially weighted moving variance uses exponential smoothing to calculate variance with the formula:
\[EWMV_t = \alpha \sum_{i=0}^{t} (1-\alpha)^i (P_{t-i} - EWMA_t)^2\]where \(\alpha = \frac{2}{span + 1}\) and span is the window_size.
Key properties: - Always non-negative (variance cannot be negative) - More responsive to recent volatility changes than rolling variance - Relationship: \(EWMV = EWMSTD^2\) - Units are squared (e.g., squared dollars for price data)
Higher variance values indicate increased volatility and risk. EWMV is commonly used for: - Volatility estimation in risk management - Detecting regime changes in market conditions - Building adaptive trading strategies - Calculating value-at-risk (VaR) metrics
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewmv(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate exponentially weighted moving variance:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104]) >>> ewmv = prices.rhoa.indicators.ewmv(window_size=5) >>> print(f"Latest variance: {ewmv.iloc[-1]:.2f}") Latest variance: 6.24
Detect periods of high volatility:
>>> prices = pd.Series([100, 102, 101, 103, 105, 104, 110, 95, 105, 100]) >>> ewmv = prices.rhoa.indicators.ewmv(window_size=5) >>> high_volatility = ewmv > ewmv.rolling(20).mean() * 1.5
- ewmstd(window_size=20, adjust=True, min_periods=None, **kwargs)[source]
Calculate the exponentially weighted moving standard deviation (EWMSTD).
EWMSTD is a statistical measure that weights recent data points more heavily to provide a smoothed calculation of the moving standard deviation. This makes it more responsive to recent volatility changes compared to traditional rolling standard deviation, while maintaining smoothness.
- Parameters:
window_size (int, default 20) – The span or window size for the exponentially weighted moving calculation. Smaller spans apply heavier weighting to more recent data points and react faster to changes, while larger spans provide smoother results.
adjust (bool, default True) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the exponentially weighted moving standard deviation values with the same index as the input series.
- Return type:
See also
ewmvExponential Weighted Moving Variance
ewmaExponential Weighted Moving Average
bollinger_bandsUses standard deviation for volatility bands
atrAverage True Range for volatility measurement
Notes
The exponentially weighted moving standard deviation is the square root of the exponentially weighted moving variance:
\[EWMSTD_t = \sqrt{EWMV_t}\]where \(EWMV_t\) is calculated with exponential weights.
The relationship \(EWMSTD^2 = EWMV\) always holds.
Key characteristics: - Always non-negative (standard deviation cannot be negative) - Same units as the original series (unlike variance) - More responsive to recent volatility than rolling standard deviation - Commonly used as a volatility proxy in trading
EWMSTD is commonly used for: - Volatility-based position sizing - Risk management and stop-loss placement - Adaptive trading strategies that respond to volatility - Bollinger Bands and other volatility indicators - Normalized price movements (z-scores)
Higher values indicate increased volatility and uncertainty.
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewmstd(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate exponentially weighted moving standard deviation:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104]) >>> ewmstd = prices.rhoa.indicators.ewmstd(window_size=5) >>> print(f"Latest volatility: {ewmstd.iloc[-1]:.2f}") Latest volatility: 2.50
Use EWMSTD for volatility-adjusted position sizing:
>>> prices = pd.Series([100, 102, 104, 106, 108, 110, 112]) >>> volatility = prices.rhoa.indicators.ewmstd(window_size=10) >>> position_size = 1000 / volatility # Risk-adjusted sizing
- rsi(window_size=14, edge_case_value=100.0, **kwargs)[source]
Calculate the Relative Strength Index (RSI) for momentum analysis.
RSI is a momentum oscillator that measures the speed and magnitude of price changes on a scale of 0 to 100. Developed by J. Welles Wilder Jr., it helps identify overbought and oversold conditions, as well as potential trend reversals. RSI is one of the most widely used technical indicators in trading.
- Parameters:
window_size (int, default 14) – The size of the rolling window used to calculate the exponential moving averages of gains and losses. Traditional value is 14 periods as recommended by Wilder.
edge_case_value (float, default 100.0) – The RSI value to use when avg_loss == 0 (no losses occurred in the period). Common values are 100.0 (infinite RS, default), 50.0 (neutral), or numpy.nan.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing RSI values between 0 and 100 with the same index as the input series.
- Return type:
See also
stochasticSimilar momentum oscillator
cciCommodity Channel Index for momentum
williams_rWilliams %R momentum indicator
macdMoving Average Convergence Divergence
Notes
The Relative Strength Index is calculated using:
\[RSI = 100 - \frac{100}{1 + RS}\]where \(RS = \frac{EMA(gains)}{EMA(losses)}\) and EMA is the exponential moving average over the specified window_size.
Traditional interpretation levels: - RSI > 70: Overbought condition (potential sell signal) - RSI < 30: Oversold condition (potential buy signal) - RSI = 50: Neutral momentum (balance between bulls and bears)
Key characteristics: - Range: 0 to 100 (bounded oscillator) - Mean-reverting: tends to oscillate around 50 - Leading indicator: can signal reversals before price - Works best in ranging markets (less reliable in strong trends)
Advanced RSI techniques: - Divergence: RSI diverging from price can signal reversals - Failure swings: RSI patterns that don’t confirm new price highs/lows - Centerline crossovers: RSI crossing 50 confirms trend direction - Dynamic thresholds: Use 80/20 in strong trends instead of 70/30
The first window_size values will be NaN as the indicator requires sufficient data to calculate the initial exponential moving averages.
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.rsi(window_size=14)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 14-period RSI and identify trading signals:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110, 109]) >>> rsi = prices.rhoa.indicators.rsi(window_size=14) >>> overbought = rsi > 70 # Potential sell signals >>> oversold = rsi < 30 # Potential buy signals >>> print(f"Latest RSI: {rsi.iloc[-1]:.1f}") Latest RSI: 75.2
Detect RSI divergence for reversal signals:
>>> prices = pd.Series([100, 105, 110, 115, 120, 118, 116, 114]) >>> rsi = prices.rhoa.indicators.rsi() >>> # Bearish divergence: price makes new high but RSI doesn't >>> price_higher = prices > prices.shift(1).rolling(5).max() >>> rsi_lower = rsi < rsi.shift(1).rolling(5).max() >>> divergence = price_higher & rsi_lower
- macd(short_window=12, long_window=26, signal_window=9, **kwargs)[source]
Calculate the MACD (Moving Average Convergence Divergence) indicator.
MACD is a trend-following momentum indicator that shows the relationship between two exponential moving averages of a security’s price. Developed by Gerald Appel, it consists of three components that together provide insights into trend direction, momentum strength, and potential reversals.
- Parameters:
short_window (int, default 12) – Length of the short-term (fast) EMA window in periods. Smaller values make MACD more responsive to recent price changes.
long_window (int, default 26) – Length of the long-term (slow) EMA window in periods. Larger values provide more smoothing and stability.
signal_window (int, default 9) – Length of the signal line EMA window in periods. This smooths the MACD line to generate trading signals.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A DataFrame with three columns: - ‘macd’ : The MACD line (short_ema - long_ema) - ‘signal’ : The signal line (EMA of MACD line) - ‘histogram’ : The MACD histogram (macd - signal)
- Return type:
See also
Notes
The MACD indicator components are calculated as:
\[MACD_{line} = EMA_{short} - EMA_{long}\]\[Signal_{line} = EMA_{signal}(MACD_{line})\]\[Histogram = MACD_{line} - Signal_{line}\]Traditional interpretation: - MACD line crosses above signal: Bullish signal (buy) - MACD line crosses below signal: Bearish signal (sell) - Histogram > 0: MACD above signal (bullish momentum) - Histogram < 0: MACD below signal (bearish momentum) - Histogram expanding: Momentum increasing - Histogram contracting: Momentum decreasing
Key characteristics: - Unbounded oscillator (can take any value) - Combines trend-following and momentum aspects - Three signals: crossovers, divergences, and rapid rises/falls - Works best in trending markets
Advanced MACD techniques: - Divergence: MACD diverging from price signals potential reversals - Zero-line crossovers: MACD crossing zero indicates trend change - Histogram analysis: Momentum changes before MACD line crosses - Multiple timeframe confirmation
The standard parameters (12, 26, 9) were optimized for daily charts but can be adjusted for different timeframes or market characteristics.
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.macd()which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate MACD and identify bullish crossover:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110]) >>> macd_data = prices.rhoa.indicators.macd() >>> # Bullish signal: MACD crosses above signal >>> bullish = (macd_data['macd'] > macd_data['signal']) & ... (macd_data['macd'].shift(1) <= macd_data['signal'].shift(1)) >>> print(f"MACD: {macd_data['macd'].iloc[-1]:.3f}") MACD: 0.245
Analyze MACD histogram for momentum changes:
>>> macd_data = prices.rhoa.indicators.macd() >>> histogram = macd_data['histogram'] >>> momentum_increasing = histogram > histogram.shift(1) >>> momentum_peak = (histogram.shift(1) > histogram) & (histogram.shift(1) > histogram.shift(2))
- bollinger_bands(window_size=20, num_std=2.0, min_periods=None, center=False, **kwargs)[source]
Calculate Bollinger Bands for volatility and mean reversion analysis.
Bollinger Bands consist of three lines: an upper band, middle band (SMA), and lower band. Developed by John Bollinger, the bands expand and contract based on market volatility, providing insights into potential overbought/ oversold conditions, volatility patterns, and mean reversion opportunities.
- Parameters:
window_size (int, default 20) – The size of the rolling window used for computing the moving average and standard deviation. Standard setting is 20 periods.
num_std (float, default 2.0) – The number of standard deviations to add/subtract from the moving average to calculate the upper and lower bands. Standard setting is 2.0.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to window_size.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A DataFrame with three columns: - ‘upper_band’ : Upper Bollinger Band (middle + num_std * std) - ‘middle_band’ : Middle band (SMA of the series) - ‘lower_band’ : Lower Bollinger Band (middle - num_std * std)
- Return type:
See also
Notes
Bollinger Bands are calculated using:
\[Middle_{band} = SMA(price, window)\]\[Upper_{band} = Middle_{band} + (num\_std \times \sigma)\]\[Lower_{band} = Middle_{band} - (num\_std \times \sigma)\]where \(\sigma\) is the standard deviation over the window.
Traditional interpretation: - Price touching upper band: Potentially overbought (high relative price) - Price touching lower band: Potentially oversold (low relative price) - Price between bands: Normal trading range - Band width: Measure of volatility
Key characteristics: - Approximately 95% of price action occurs within 2 standard deviations - Bands are dynamic support/resistance levels - Band width reflects market volatility - Works as both a trend and volatility indicator
Common Bollinger Band strategies: - Squeeze: Narrow bands indicate low volatility, often precedes breakout - Expansion: Wide bands indicate high volatility - Band walk: Price riding upper/lower band indicates strong trend - Bollinger Bounce: Mean reversion trades off band touches - %B indicator: (price - lower) / (upper - lower) shows relative position
Advanced techniques: - Double tops/bottoms at bands for reversal signals - M-tops and W-bottoms for patterns - Band width as volatility indicator - Combination with other indicators for confirmation
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.bollinger_bands(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate Bollinger Bands and identify squeeze conditions:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107]) >>> bb = prices.rhoa.indicators.bollinger_bands(window_size=5, num_std=2.0) >>> # Band width indicates volatility >>> width = bb['upper_band'] - bb['lower_band'] >>> squeeze = width < width.rolling(10).mean() * 0.8 # Low volatility >>> print(f"Upper: {bb['upper_band'].iloc[-1]:.2f}") Upper: 109.45
Calculate %B indicator for position within bands:
>>> bb = prices.rhoa.indicators.bollinger_bands() >>> percent_b = (prices - bb['lower_band']) / (bb['upper_band'] - bb['lower_band']) >>> overbought = percent_b > 1.0 # Price above upper band >>> oversold = percent_b < 0.0 # Price below lower band
- class DataFrameIndicators[source]
Bases:
objectDataFrame-level indicators accessor for OHLC operations.
Auto-detects Close, High, and Low columns from the DataFrame, delegating computation to the existing
indicatorsclass.- bollinger_bands(close=None, window_size=20, num_std=2.0, min_periods=None, center=False, **kwargs)[source]
- atr(close=None, high=None, low=None, window_size=14, min_periods=None, center=False, **kwargs)[source]
Calculate the Average True Range (ATR) for volatility measurement.
ATR is a volatility indicator developed by J. Welles Wilder Jr. that measures the degree of price movement by decomposing the entire range of an asset for a given period. It accounts for gaps between sessions by using true range rather than simple high-low range. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 14) – Length of the rolling window for calculating the average true range.
min_periods (int, optional) – Minimum number of observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated ATR values.
- Return type:
See also
bollinger_bandsVolatility bands using standard deviation
ewmstdExponential weighted moving standard deviation
adxAverage Directional Index, uses ATR internally
Notes
The True Range (TR) is first calculated as the greatest of:
\[TR_t = \max(H_t - L_t,\; |H_t - C_{t-1}|,\; |L_t - C_{t-1}|)\]where \(H_t\) is the high, \(L_t\) is the low, and \(C_{t-1}\) is the previous close.
The ATR is then the simple moving average of the true range:
\[ATR_t = \frac{1}{n} \sum_{i=0}^{n-1} TR_{t-i}\]where n is the window_size.
Key characteristics: - ATR measures volatility, not price direction - Higher ATR values indicate higher volatility - ATR is always positive (absolute price movement) - Useful for setting stop-loss levels and position sizing
Common applications: - Setting trailing stops at a multiple of ATR (e.g., 2x ATR) - Position sizing: smaller positions when ATR is high - Identifying breakouts: volatility expansion signals trend starts - Comparing volatility across different instruments
References
Examples
Calculate 14-period ATR on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115], ... 'Low': [100, 102, 101, 103, 105], ... 'Close': [105, 108, 106, 110, 112] ... }) >>> atr = df.rhoa.indicators.atr(window_size=3) >>> print(f"Latest ATR: {atr.iloc[-1]:.2f}") Latest ATR: 10.00
Use ATR for setting stop-loss levels:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 51, 53, 55, 54, 56], ... 'Low': [48, 49, 48, 50, 52, 51, 53], ... 'Close': [49, 51, 50, 52, 54, 53, 55] ... }) >>> atr = df.rhoa.indicators.atr(window_size=5) >>> stop_loss = df['Close'] - 2 * atr # Trailing stop at 2x ATR
- cci(close=None, high=None, low=None, window_size=20, min_periods=None, center=False, **kwargs)[source]
Calculate the Commodity Channel Index (CCI) for momentum analysis.
CCI is a versatile momentum oscillator developed by Donald Lambert that measures the deviation of price from its statistical mean. It is used to identify cyclical trends, overbought/oversold conditions, and potential reversals. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 20) – Number of periods for calculating the CCI.
min_periods (int, optional) – Minimum number of observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated CCI values.
- Return type:
See also
rsiRelative Strength Index for momentum
stochasticStochastic Oscillator for momentum
williams_rWilliams %R momentum indicator
Notes
The Typical Price (TP) is first calculated:
\[TP_t = \frac{H_t + L_t + C_t}{3}\]The CCI is then:
\[CCI_t = \frac{TP_t - SMA(TP, n)}{0.015 \times MD_t}\]where \(SMA(TP, n)\) is the simple moving average of typical price over n periods and \(MD_t\) is the mean absolute deviation:
\[MD_t = \frac{1}{n} \sum_{i=0}^{n-1} |TP_{t-i} - SMA(TP, n)|\]The constant 0.015 is chosen so that approximately 70-80% of CCI values fall between -100 and +100.
Traditional interpretation: - CCI > +100: Overbought territory (potential sell signal) - CCI < -100: Oversold territory (potential buy signal) - CCI crossing zero: Trend direction confirmation
Common applications: - Identifying new trends when CCI moves above +100 or below -100 - Divergence detection between CCI and price - Zero-line crossovers for trend confirmation
References
Examples
Calculate 20-period CCI on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115, 114, 116], ... 'Low': [100, 102, 101, 103, 105, 104, 106], ... 'Close': [105, 108, 106, 110, 112, 109, 113] ... }) >>> cci = df.rhoa.indicators.cci(window_size=5)
Identify overbought and oversold conditions:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 56, 58, 55, 53, 51, 49, 47], ... 'Low': [48, 49, 51, 53, 55, 52, 50, 48, 46, 44], ... 'Close': [49, 51, 53, 55, 57, 54, 52, 50, 48, 46] ... }) >>> cci = df.rhoa.indicators.cci(window_size=5) >>> overbought = cci > 100 >>> oversold = cci < -100
- stochastic(close=None, high=None, low=None, k_window=14, d_window=3, min_periods=None, center=False, **kwargs)[source]
Calculate the Stochastic Oscillator (%K and %D) for momentum analysis.
The Stochastic Oscillator is a momentum indicator developed by George Lane that compares a security’s closing price to its price range over a given period. It is based on the observation that in an uptrend, closing prices tend to close near the high, and in a downtrend, near the low. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
k_window (int, default 14) – Number of periods for %K calculation.
d_window (int, default 3) – Number of periods for %D calculation (SMA of %K).
min_periods (int, optional) – Minimum observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A DataFrame with ‘%K’ and ‘%D’ columns.
- Return type:
See also
rsiRelative Strength Index for momentum
williams_rWilliams %R, closely related momentum oscillator
cciCommodity Channel Index for momentum
Notes
The %K (fast stochastic) is calculated as:
\[\%K = 100 \times \frac{C_t - L_n}{H_n - L_n}\]where \(C_t\) is the current close, \(L_n\) is the lowest low over the k_window periods, and \(H_n\) is the highest high over the k_window periods.
The %D (slow stochastic / signal line) is a simple moving average of %K:
\[\%D = SMA(\%K, d)\]where d is the d_window.
Traditional interpretation: - %K or %D > 80: Overbought territory (potential sell signal) - %K or %D < 20: Oversold territory (potential buy signal) - %K crossing above %D: Bullish signal - %K crossing below %D: Bearish signal
Key characteristics: - Range: 0 to 100 (bounded oscillator) - %K is more sensitive and reacts faster than %D - Works best in ranging/sideways markets - Divergence between stochastic and price can signal reversals
Examples
Calculate the Stochastic Oscillator on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115, 114, 116], ... 'Low': [100, 102, 101, 103, 105, 104, 106], ... 'Close': [105, 108, 106, 110, 112, 109, 113] ... }) >>> stoch = df.rhoa.indicators.stochastic(k_window=5, d_window=3) >>> print(stoch.columns.tolist()) ['%K', '%D']
Generate crossover signals:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 53, 55, 54, 56, 55, 57, 56], ... 'Low': [48, 49, 51, 50, 52, 51, 53, 52, 54, 53], ... 'Close': [49, 51, 53, 52, 54, 53, 55, 54, 56, 55] ... }) >>> stoch = df.rhoa.indicators.stochastic(k_window=5) >>> buy = (stoch['%K'] > stoch['%D']) & (stoch['%K'].shift(1) <= stoch['%D'].shift(1))
- williams_r(close=None, high=None, low=None, window_size=14, min_periods=None, center=False, **kwargs)[source]
Calculate Williams %R for momentum and overbought/oversold analysis.
Williams %R is a momentum indicator developed by Larry Williams that measures overbought and oversold levels on a scale from -100 to 0. It is the inverse of the Fast Stochastic Oscillator and reflects the level of the close relative to the highest high over the lookback period. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 14) – Number of periods for Williams %R calculation.
min_periods (int, optional) – Minimum observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing Williams %R values ranging from -100 to 0.
- Return type:
See also
stochasticStochastic Oscillator, closely related indicator
rsiRelative Strength Index for momentum
cciCommodity Channel Index for momentum
Notes
Williams %R is calculated as:
\[\%R = -100 \times \frac{H_n - C_t}{H_n - L_n}\]where \(C_t\) is the current close, \(H_n\) is the highest high over the window_size periods, and \(L_n\) is the lowest low over the window_size periods.
Williams %R is mathematically related to the Stochastic Oscillator:
\[\%R = \%K - 100\]Traditional interpretation: - %R between -20 and 0: Overbought (potential sell signal) - %R between -100 and -80: Oversold (potential buy signal) - %R = 0: Close equals the highest high of the period - %R = -100: Close equals the lowest low of the period
Key characteristics: - Range: -100 to 0 (bounded oscillator, negative scale) - Leading indicator: can signal reversals before price - More responsive than RSI to short-term price changes - Works best in ranging markets; use with trend filters
Examples
Calculate 14-period Williams %R:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115, 114, 116], ... 'Low': [100, 102, 101, 103, 105, 104, 106], ... 'Close': [105, 108, 106, 110, 112, 109, 113] ... }) >>> wr = df.rhoa.indicators.williams_r(window_size=5)
Identify overbought and oversold conditions:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 53, 55, 54, 56, 55, 57, 56], ... 'Low': [48, 49, 51, 50, 52, 51, 53, 52, 54, 53], ... 'Close': [49, 51, 53, 52, 54, 53, 55, 54, 56, 55] ... }) >>> wr = df.rhoa.indicators.williams_r(window_size=5) >>> overbought = wr > -20 >>> oversold = wr < -80
- adx(close=None, high=None, low=None, window_size=14, min_periods=None, **kwargs)[source]
Calculate the Average Directional Index (ADX) for trend strength analysis.
ADX is a trend strength indicator developed by J. Welles Wilder Jr. that quantifies the strength of a trend regardless of its direction. It combines the Plus Directional Indicator (+DI) and Minus Directional Indicator (-DI) to measure how strongly price is moving in one direction. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 14) – Number of periods for ADX calculation.
min_periods (int, optional) – Minimum observations in window required to have a value.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A DataFrame with ‘ADX’, ‘+DI’, and ‘-DI’ columns.
- Return type:
See also
atrAverage True Range, used internally by ADX
rsiRelative Strength Index for momentum
parabolic_sarParabolic SAR for trend following
Notes
The calculation involves several steps:
Directional Movement (DM):
\[\begin{split}+DM_t = \begin{cases} H_t - H_{t-1} & \text{if } H_t - H_{t-1} > L_{t-1} - L_t \text{ and } H_t - H_{t-1} > 0 \\ 0 & \text{otherwise} \end{cases}\end{split}\]\[\begin{split}-DM_t = \begin{cases} L_{t-1} - L_t & \text{if } L_{t-1} - L_t > H_t - H_{t-1} \text{ and } L_{t-1} - L_t > 0 \\ 0 & \text{otherwise} \end{cases}\end{split}\]Directional Indicators (DI):
\[+DI = 100 \times \frac{EMA(+DM, n)}{EMA(TR, n)}\]\[-DI = 100 \times \frac{EMA(-DM, n)}{EMA(TR, n)}\]Directional Index (DX) and ADX:
\[DX = 100 \times \frac{|{+DI} - {-DI}|}{+DI + {-DI}}\]\[ADX = EMA(DX, n)\]Traditional interpretation: - ADX > 25: Strong trend (consider trend-following strategies) - ADX < 20: Weak trend or ranging market (consider oscillator strategies) - +DI > -DI: Uptrend (bullish) - -DI > +DI: Downtrend (bearish) - +DI crossing above -DI: Bullish crossover signal - -DI crossing above +DI: Bearish crossover signal
Key characteristics: - ADX measures trend strength, not direction - Rising ADX = strengthening trend; falling ADX = weakening trend - ADX is a lagging indicator due to smoothing
References
Examples
Calculate 14-period ADX on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 114, 113, 115, 117, 116], ... 'Low': [100, 102, 104, 103, 105, 107, 106], ... 'Close': [105, 108, 110, 109, 112, 114, 113] ... }) >>> result = df.rhoa.indicators.adx(window_size=5) >>> print(result.columns.tolist()) ['ADX', '+DI', '-DI']
Identify strong trends and crossover signals:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 56, 58, 57, 55, 53, 51, 49], ... 'Low': [48, 49, 51, 53, 55, 54, 52, 50, 48, 46], ... 'Close': [49, 51, 53, 55, 57, 56, 54, 52, 50, 48] ... }) >>> result = df.rhoa.indicators.adx(window_size=5) >>> strong_trend = result['ADX'] > 25 >>> bullish = result['+DI'] > result['-DI']
- parabolic_sar(close=None, high=None, low=None, af_start=0.02, af_increment=0.02, af_maximum=0.2)[source]
Calculate the Parabolic Stop and Reverse (SAR) for trend following.
Parabolic SAR is a trend-following indicator developed by J. Welles Wilder Jr. that provides potential entry and exit points. It appears as a series of dots placed above or below the price, indicating bearish or bullish conditions respectively. The “parabolic” name comes from the parabola-shaped curve the dots form as a trend develops. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
af_start (float, default 0.02) – Initial acceleration factor.
af_increment (float, default 0.02) – Increment added to acceleration factor when a new extreme point is reached.
af_maximum (float, default 0.2) – Maximum acceleration factor value.
- Returns:
A Series containing Parabolic SAR values.
- Return type:
See also
Notes
The Parabolic SAR is calculated iteratively:
\[SAR_{t+1} = SAR_t + AF \times (EP - SAR_t)\]where: - \(SAR_t\) is the current SAR value - \(AF\) is the acceleration factor, starting at af_start and
increasing by af_increment each time a new extreme point is made, up to af_maximum
\(EP\) is the extreme point (highest high in uptrend, lowest low in downtrend)
Trend reversal occurs when price crosses the SAR value: - In an uptrend, if the low touches or falls below SAR, the trend
reverses to downtrend
In a downtrend, if the high touches or rises above SAR, the trend reverses to uptrend
Upon reversal, the SAR is set to the previous extreme point and the acceleration factor resets to af_start.
Key characteristics: - SAR below price = uptrend (bullish) - SAR above price = downtrend (bearish) - SAR accelerates toward price as a trend develops - Works best in trending markets; can whipsaw in sideways markets
Common applications: - Setting trailing stop-loss orders - Determining trend direction - Identifying potential reversal points - Combining with ADX to filter for strong trends
References
Examples
Calculate Parabolic SAR with default parameters:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 114, 113, 115, 117, 116], ... 'Low': [100, 102, 104, 103, 105, 107, 106], ... 'Close': [105, 108, 110, 109, 112, 114, 113] ... }) >>> sar = df.rhoa.indicators.parabolic_sar()
Use SAR to determine trend direction:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 53, 55, 54, 56, 55, 57, 56], ... 'Low': [48, 49, 51, 50, 52, 51, 53, 52, 54, 53], ... 'Close': [49, 51, 53, 52, 54, 53, 55, 54, 56, 55] ... }) >>> sar = df.rhoa.indicators.parabolic_sar(af_start=0.02, af_maximum=0.2) >>> uptrend = df['Close'] > sar >>> downtrend = df['Close'] < sar
The indicators module provides technical analysis indicators through pandas DataFrame and Series accessors.
indicators Class
- class indicators[source]
Bases:
object- sma(window_size=20, min_periods=None, center=False, **kwargs)[source]
Calculate the Simple Moving Average (SMA) over a specified window.
The SMA is a commonly used technical indicator in financial and time series analysis that calculates the arithmetic mean of prices over a defined number of periods. It smooths out price data to identify trends by reducing noise from short-term fluctuations.
- Parameters:
window_size (int, default 20) – The size of the moving window, representing the number of periods over which to calculate the average.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to window_size.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated SMA values with the same index as the input series.
- Return type:
See also
ewmaExponential Weighted Moving Average for trend analysis
bollinger_bandsUses SMA as the middle band
macdUses exponential moving averages
Notes
The Simple Moving Average is calculated as:
\[SMA_t = \frac{1}{n} \sum_{i=0}^{n-1} P_{t-i}\]where \(P_t\) is the price at time t and n is the window_size.
The first window_size - 1 values will be NaN unless min_periods is set to a lower value. SMA gives equal weight to all values in the window, which can make it slower to respond to recent price changes compared to exponential moving averages.
SMA is commonly used for: - Identifying support and resistance levels - Generating crossover trading signals (e.g., golden cross, death cross) - Smoothing price data for trend identification
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.sma(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 20-period Simple Moving Average:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106]) >>> sma = prices.rhoa.indicators.sma(window_size=5) >>> print(sma.iloc[4]) # First valid SMA value 102.2
Generate trading signals using SMA crossover:
>>> prices = pd.Series([100, 102, 104, 106, 108, 107, 105, 103, 101]) >>> sma_short = prices.rhoa.indicators.sma(window_size=3) >>> sma_long = prices.rhoa.indicators.sma(window_size=5) >>> buy_signal = (sma_short > sma_long) & (sma_short.shift(1) <= sma_long.shift(1))
- ewma(window_size=20, adjust=False, min_periods=None, **kwargs)[source]
Calculate the Exponential Weighted Moving Average (EWMA) of the series.
The EWMA is a type of infinite impulse response filter that applies weighting factors which decrease exponentially. Unlike simple moving averages, EWMA gives more weight to recent observations, making it more responsive to recent price changes while still providing smoothing.
- Parameters:
window_size (int, default 20) – The span of the exponential moving average. Determines the level of smoothing, where larger values result in smoother trends and slower responsiveness to changes in the data.
adjust (bool, default False) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights to account for the imbalance in the beginning periods.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the calculated EWMA values with the same index as the input series.
- Return type:
See also
Notes
The Exponential Weighted Moving Average is calculated using:
\[EWMA_t = \alpha \cdot P_t + (1 - \alpha) \cdot EWMA_{t-1}\]where \(\alpha = \frac{2}{span + 1}\) and span is the window_size.
Key characteristics: - More weight to recent prices: reacts faster to recent changes - Smoother than price but more responsive than SMA - All historical data has some influence (infinite impulse response) - No lookback period required (unlike SMA)
The adjust parameter affects the calculation in the initial periods: - adjust=True: Uses normalized weights (standard EWMA definition) - adjust=False: Uses recursive formula (more common in trading)
EWMA is commonly used for: - Trend identification and confirmation - Support and resistance levels that adapt to volatility - Component of MACD and other composite indicators
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewma(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 20-period Exponential Weighted Moving Average:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106, 108]) >>> ewma = prices.rhoa.indicators.ewma(window_size=5) >>> print(f"Latest EWMA: {ewma.iloc[-1]:.2f}") Latest EWMA: 105.45
Compare EWMA with different window sizes:
>>> ewma_fast = prices.rhoa.indicators.ewma(window_size=5) >>> ewma_slow = prices.rhoa.indicators.ewma(window_size=20) >>> crossover = (ewma_fast > ewma_slow) & (ewma_fast.shift(1) <= ewma_slow.shift(1))
- ewmv(window_size=20, adjust=True, min_periods=None, **kwargs)[source]
Calculate the exponentially weighted moving variance (EWMV) of a series.
This method computes the variance of a series by applying exponential weighting to give more importance to recent observations. EWMV is useful for measuring volatility that adapts more quickly to recent price changes compared to standard rolling variance.
- Parameters:
window_size (int, default 20) – The span of the exponential window. Determines the level of smoothing applied to the variance calculation. Larger values result in smoother variance estimates.
adjust (bool, default True) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the exponentially weighted moving variance values with the same index as the input series.
- Return type:
See also
ewmstdExponential Weighted Moving Standard Deviation
ewmaExponential Weighted Moving Average
bollinger_bandsUses standard deviation for band calculation
Notes
The exponentially weighted moving variance uses exponential smoothing to calculate variance with the formula:
\[EWMV_t = \alpha \sum_{i=0}^{t} (1-\alpha)^i (P_{t-i} - EWMA_t)^2\]where \(\alpha = \frac{2}{span + 1}\) and span is the window_size.
Key properties: - Always non-negative (variance cannot be negative) - More responsive to recent volatility changes than rolling variance - Relationship: \(EWMV = EWMSTD^2\) - Units are squared (e.g., squared dollars for price data)
Higher variance values indicate increased volatility and risk. EWMV is commonly used for: - Volatility estimation in risk management - Detecting regime changes in market conditions - Building adaptive trading strategies - Calculating value-at-risk (VaR) metrics
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewmv(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate exponentially weighted moving variance:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104]) >>> ewmv = prices.rhoa.indicators.ewmv(window_size=5) >>> print(f"Latest variance: {ewmv.iloc[-1]:.2f}") Latest variance: 6.24
Detect periods of high volatility:
>>> prices = pd.Series([100, 102, 101, 103, 105, 104, 110, 95, 105, 100]) >>> ewmv = prices.rhoa.indicators.ewmv(window_size=5) >>> high_volatility = ewmv > ewmv.rolling(20).mean() * 1.5
- ewmstd(window_size=20, adjust=True, min_periods=None, **kwargs)[source]
Calculate the exponentially weighted moving standard deviation (EWMSTD).
EWMSTD is a statistical measure that weights recent data points more heavily to provide a smoothed calculation of the moving standard deviation. This makes it more responsive to recent volatility changes compared to traditional rolling standard deviation, while maintaining smoothness.
- Parameters:
window_size (int, default 20) – The span or window size for the exponentially weighted moving calculation. Smaller spans apply heavier weighting to more recent data points and react faster to changes, while larger spans provide smoother results.
adjust (bool, default True) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the exponentially weighted moving standard deviation values with the same index as the input series.
- Return type:
See also
ewmvExponential Weighted Moving Variance
ewmaExponential Weighted Moving Average
bollinger_bandsUses standard deviation for volatility bands
atrAverage True Range for volatility measurement
Notes
The exponentially weighted moving standard deviation is the square root of the exponentially weighted moving variance:
\[EWMSTD_t = \sqrt{EWMV_t}\]where \(EWMV_t\) is calculated with exponential weights.
The relationship \(EWMSTD^2 = EWMV\) always holds.
Key characteristics: - Always non-negative (standard deviation cannot be negative) - Same units as the original series (unlike variance) - More responsive to recent volatility than rolling standard deviation - Commonly used as a volatility proxy in trading
EWMSTD is commonly used for: - Volatility-based position sizing - Risk management and stop-loss placement - Adaptive trading strategies that respond to volatility - Bollinger Bands and other volatility indicators - Normalized price movements (z-scores)
Higher values indicate increased volatility and uncertainty.
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewmstd(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate exponentially weighted moving standard deviation:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104]) >>> ewmstd = prices.rhoa.indicators.ewmstd(window_size=5) >>> print(f"Latest volatility: {ewmstd.iloc[-1]:.2f}") Latest volatility: 2.50
Use EWMSTD for volatility-adjusted position sizing:
>>> prices = pd.Series([100, 102, 104, 106, 108, 110, 112]) >>> volatility = prices.rhoa.indicators.ewmstd(window_size=10) >>> position_size = 1000 / volatility # Risk-adjusted sizing
- rsi(window_size=14, edge_case_value=100.0, **kwargs)[source]
Calculate the Relative Strength Index (RSI) for momentum analysis.
RSI is a momentum oscillator that measures the speed and magnitude of price changes on a scale of 0 to 100. Developed by J. Welles Wilder Jr., it helps identify overbought and oversold conditions, as well as potential trend reversals. RSI is one of the most widely used technical indicators in trading.
- Parameters:
window_size (int, default 14) – The size of the rolling window used to calculate the exponential moving averages of gains and losses. Traditional value is 14 periods as recommended by Wilder.
edge_case_value (float, default 100.0) – The RSI value to use when avg_loss == 0 (no losses occurred in the period). Common values are 100.0 (infinite RS, default), 50.0 (neutral), or numpy.nan.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing RSI values between 0 and 100 with the same index as the input series.
- Return type:
See also
stochasticSimilar momentum oscillator
cciCommodity Channel Index for momentum
williams_rWilliams %R momentum indicator
macdMoving Average Convergence Divergence
Notes
The Relative Strength Index is calculated using:
\[RSI = 100 - \frac{100}{1 + RS}\]where \(RS = \frac{EMA(gains)}{EMA(losses)}\) and EMA is the exponential moving average over the specified window_size.
Traditional interpretation levels: - RSI > 70: Overbought condition (potential sell signal) - RSI < 30: Oversold condition (potential buy signal) - RSI = 50: Neutral momentum (balance between bulls and bears)
Key characteristics: - Range: 0 to 100 (bounded oscillator) - Mean-reverting: tends to oscillate around 50 - Leading indicator: can signal reversals before price - Works best in ranging markets (less reliable in strong trends)
Advanced RSI techniques: - Divergence: RSI diverging from price can signal reversals - Failure swings: RSI patterns that don’t confirm new price highs/lows - Centerline crossovers: RSI crossing 50 confirms trend direction - Dynamic thresholds: Use 80/20 in strong trends instead of 70/30
The first window_size values will be NaN as the indicator requires sufficient data to calculate the initial exponential moving averages.
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.rsi(window_size=14)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 14-period RSI and identify trading signals:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110, 109]) >>> rsi = prices.rhoa.indicators.rsi(window_size=14) >>> overbought = rsi > 70 # Potential sell signals >>> oversold = rsi < 30 # Potential buy signals >>> print(f"Latest RSI: {rsi.iloc[-1]:.1f}") Latest RSI: 75.2
Detect RSI divergence for reversal signals:
>>> prices = pd.Series([100, 105, 110, 115, 120, 118, 116, 114]) >>> rsi = prices.rhoa.indicators.rsi() >>> # Bearish divergence: price makes new high but RSI doesn't >>> price_higher = prices > prices.shift(1).rolling(5).max() >>> rsi_lower = rsi < rsi.shift(1).rolling(5).max() >>> divergence = price_higher & rsi_lower
- macd(short_window=12, long_window=26, signal_window=9, **kwargs)[source]
Calculate the MACD (Moving Average Convergence Divergence) indicator.
MACD is a trend-following momentum indicator that shows the relationship between two exponential moving averages of a security’s price. Developed by Gerald Appel, it consists of three components that together provide insights into trend direction, momentum strength, and potential reversals.
- Parameters:
short_window (int, default 12) – Length of the short-term (fast) EMA window in periods. Smaller values make MACD more responsive to recent price changes.
long_window (int, default 26) – Length of the long-term (slow) EMA window in periods. Larger values provide more smoothing and stability.
signal_window (int, default 9) – Length of the signal line EMA window in periods. This smooths the MACD line to generate trading signals.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A DataFrame with three columns: - ‘macd’ : The MACD line (short_ema - long_ema) - ‘signal’ : The signal line (EMA of MACD line) - ‘histogram’ : The MACD histogram (macd - signal)
- Return type:
See also
Notes
The MACD indicator components are calculated as:
\[MACD_{line} = EMA_{short} - EMA_{long}\]\[Signal_{line} = EMA_{signal}(MACD_{line})\]\[Histogram = MACD_{line} - Signal_{line}\]Traditional interpretation: - MACD line crosses above signal: Bullish signal (buy) - MACD line crosses below signal: Bearish signal (sell) - Histogram > 0: MACD above signal (bullish momentum) - Histogram < 0: MACD below signal (bearish momentum) - Histogram expanding: Momentum increasing - Histogram contracting: Momentum decreasing
Key characteristics: - Unbounded oscillator (can take any value) - Combines trend-following and momentum aspects - Three signals: crossovers, divergences, and rapid rises/falls - Works best in trending markets
Advanced MACD techniques: - Divergence: MACD diverging from price signals potential reversals - Zero-line crossovers: MACD crossing zero indicates trend change - Histogram analysis: Momentum changes before MACD line crosses - Multiple timeframe confirmation
The standard parameters (12, 26, 9) were optimized for daily charts but can be adjusted for different timeframes or market characteristics.
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.macd()which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate MACD and identify bullish crossover:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110]) >>> macd_data = prices.rhoa.indicators.macd() >>> # Bullish signal: MACD crosses above signal >>> bullish = (macd_data['macd'] > macd_data['signal']) & ... (macd_data['macd'].shift(1) <= macd_data['signal'].shift(1)) >>> print(f"MACD: {macd_data['macd'].iloc[-1]:.3f}") MACD: 0.245
Analyze MACD histogram for momentum changes:
>>> macd_data = prices.rhoa.indicators.macd() >>> histogram = macd_data['histogram'] >>> momentum_increasing = histogram > histogram.shift(1) >>> momentum_peak = (histogram.shift(1) > histogram) & (histogram.shift(1) > histogram.shift(2))
- bollinger_bands(window_size=20, num_std=2.0, min_periods=None, center=False, **kwargs)[source]
Calculate Bollinger Bands for volatility and mean reversion analysis.
Bollinger Bands consist of three lines: an upper band, middle band (SMA), and lower band. Developed by John Bollinger, the bands expand and contract based on market volatility, providing insights into potential overbought/ oversold conditions, volatility patterns, and mean reversion opportunities.
- Parameters:
window_size (int, default 20) – The size of the rolling window used for computing the moving average and standard deviation. Standard setting is 20 periods.
num_std (float, default 2.0) – The number of standard deviations to add/subtract from the moving average to calculate the upper and lower bands. Standard setting is 2.0.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to window_size.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A DataFrame with three columns: - ‘upper_band’ : Upper Bollinger Band (middle + num_std * std) - ‘middle_band’ : Middle band (SMA of the series) - ‘lower_band’ : Lower Bollinger Band (middle - num_std * std)
- Return type:
See also
Notes
Bollinger Bands are calculated using:
\[Middle_{band} = SMA(price, window)\]\[Upper_{band} = Middle_{band} + (num\_std \times \sigma)\]\[Lower_{band} = Middle_{band} - (num\_std \times \sigma)\]where \(\sigma\) is the standard deviation over the window.
Traditional interpretation: - Price touching upper band: Potentially overbought (high relative price) - Price touching lower band: Potentially oversold (low relative price) - Price between bands: Normal trading range - Band width: Measure of volatility
Key characteristics: - Approximately 95% of price action occurs within 2 standard deviations - Bands are dynamic support/resistance levels - Band width reflects market volatility - Works as both a trend and volatility indicator
Common Bollinger Band strategies: - Squeeze: Narrow bands indicate low volatility, often precedes breakout - Expansion: Wide bands indicate high volatility - Band walk: Price riding upper/lower band indicates strong trend - Bollinger Bounce: Mean reversion trades off band touches - %B indicator: (price - lower) / (upper - lower) shows relative position
Advanced techniques: - Double tops/bottoms at bands for reversal signals - M-tops and W-bottoms for patterns - Band width as volatility indicator - Combination with other indicators for confirmation
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.bollinger_bands(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate Bollinger Bands and identify squeeze conditions:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107]) >>> bb = prices.rhoa.indicators.bollinger_bands(window_size=5, num_std=2.0) >>> # Band width indicates volatility >>> width = bb['upper_band'] - bb['lower_band'] >>> squeeze = width < width.rolling(10).mean() * 0.8 # Low volatility >>> print(f"Upper: {bb['upper_band'].iloc[-1]:.2f}") Upper: 109.45
Calculate %B indicator for position within bands:
>>> bb = prices.rhoa.indicators.bollinger_bands() >>> percent_b = (prices - bb['lower_band']) / (bb['upper_band'] - bb['lower_band']) >>> overbought = percent_b > 1.0 # Price above upper band >>> oversold = percent_b < 0.0 # Price below lower band
DataFrameIndicators Class
- class DataFrameIndicators[source]
Bases:
objectDataFrame-level indicators accessor for OHLC operations.
Auto-detects Close, High, and Low columns from the DataFrame, delegating computation to the existing
indicatorsclass.- bollinger_bands(close=None, window_size=20, num_std=2.0, min_periods=None, center=False, **kwargs)[source]
- atr(close=None, high=None, low=None, window_size=14, min_periods=None, center=False, **kwargs)[source]
Calculate the Average True Range (ATR) for volatility measurement.
ATR is a volatility indicator developed by J. Welles Wilder Jr. that measures the degree of price movement by decomposing the entire range of an asset for a given period. It accounts for gaps between sessions by using true range rather than simple high-low range. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 14) – Length of the rolling window for calculating the average true range.
min_periods (int, optional) – Minimum number of observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated ATR values.
- Return type:
See also
bollinger_bandsVolatility bands using standard deviation
ewmstdExponential weighted moving standard deviation
adxAverage Directional Index, uses ATR internally
Notes
The True Range (TR) is first calculated as the greatest of:
\[TR_t = \max(H_t - L_t,\; |H_t - C_{t-1}|,\; |L_t - C_{t-1}|)\]where \(H_t\) is the high, \(L_t\) is the low, and \(C_{t-1}\) is the previous close.
The ATR is then the simple moving average of the true range:
\[ATR_t = \frac{1}{n} \sum_{i=0}^{n-1} TR_{t-i}\]where n is the window_size.
Key characteristics: - ATR measures volatility, not price direction - Higher ATR values indicate higher volatility - ATR is always positive (absolute price movement) - Useful for setting stop-loss levels and position sizing
Common applications: - Setting trailing stops at a multiple of ATR (e.g., 2x ATR) - Position sizing: smaller positions when ATR is high - Identifying breakouts: volatility expansion signals trend starts - Comparing volatility across different instruments
References
Examples
Calculate 14-period ATR on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115], ... 'Low': [100, 102, 101, 103, 105], ... 'Close': [105, 108, 106, 110, 112] ... }) >>> atr = df.rhoa.indicators.atr(window_size=3) >>> print(f"Latest ATR: {atr.iloc[-1]:.2f}") Latest ATR: 10.00
Use ATR for setting stop-loss levels:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 51, 53, 55, 54, 56], ... 'Low': [48, 49, 48, 50, 52, 51, 53], ... 'Close': [49, 51, 50, 52, 54, 53, 55] ... }) >>> atr = df.rhoa.indicators.atr(window_size=5) >>> stop_loss = df['Close'] - 2 * atr # Trailing stop at 2x ATR
- cci(close=None, high=None, low=None, window_size=20, min_periods=None, center=False, **kwargs)[source]
Calculate the Commodity Channel Index (CCI) for momentum analysis.
CCI is a versatile momentum oscillator developed by Donald Lambert that measures the deviation of price from its statistical mean. It is used to identify cyclical trends, overbought/oversold conditions, and potential reversals. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 20) – Number of periods for calculating the CCI.
min_periods (int, optional) – Minimum number of observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated CCI values.
- Return type:
See also
rsiRelative Strength Index for momentum
stochasticStochastic Oscillator for momentum
williams_rWilliams %R momentum indicator
Notes
The Typical Price (TP) is first calculated:
\[TP_t = \frac{H_t + L_t + C_t}{3}\]The CCI is then:
\[CCI_t = \frac{TP_t - SMA(TP, n)}{0.015 \times MD_t}\]where \(SMA(TP, n)\) is the simple moving average of typical price over n periods and \(MD_t\) is the mean absolute deviation:
\[MD_t = \frac{1}{n} \sum_{i=0}^{n-1} |TP_{t-i} - SMA(TP, n)|\]The constant 0.015 is chosen so that approximately 70-80% of CCI values fall between -100 and +100.
Traditional interpretation: - CCI > +100: Overbought territory (potential sell signal) - CCI < -100: Oversold territory (potential buy signal) - CCI crossing zero: Trend direction confirmation
Common applications: - Identifying new trends when CCI moves above +100 or below -100 - Divergence detection between CCI and price - Zero-line crossovers for trend confirmation
References
Examples
Calculate 20-period CCI on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115, 114, 116], ... 'Low': [100, 102, 101, 103, 105, 104, 106], ... 'Close': [105, 108, 106, 110, 112, 109, 113] ... }) >>> cci = df.rhoa.indicators.cci(window_size=5)
Identify overbought and oversold conditions:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 56, 58, 55, 53, 51, 49, 47], ... 'Low': [48, 49, 51, 53, 55, 52, 50, 48, 46, 44], ... 'Close': [49, 51, 53, 55, 57, 54, 52, 50, 48, 46] ... }) >>> cci = df.rhoa.indicators.cci(window_size=5) >>> overbought = cci > 100 >>> oversold = cci < -100
- stochastic(close=None, high=None, low=None, k_window=14, d_window=3, min_periods=None, center=False, **kwargs)[source]
Calculate the Stochastic Oscillator (%K and %D) for momentum analysis.
The Stochastic Oscillator is a momentum indicator developed by George Lane that compares a security’s closing price to its price range over a given period. It is based on the observation that in an uptrend, closing prices tend to close near the high, and in a downtrend, near the low. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
k_window (int, default 14) – Number of periods for %K calculation.
d_window (int, default 3) – Number of periods for %D calculation (SMA of %K).
min_periods (int, optional) – Minimum observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A DataFrame with ‘%K’ and ‘%D’ columns.
- Return type:
See also
rsiRelative Strength Index for momentum
williams_rWilliams %R, closely related momentum oscillator
cciCommodity Channel Index for momentum
Notes
The %K (fast stochastic) is calculated as:
\[\%K = 100 \times \frac{C_t - L_n}{H_n - L_n}\]where \(C_t\) is the current close, \(L_n\) is the lowest low over the k_window periods, and \(H_n\) is the highest high over the k_window periods.
The %D (slow stochastic / signal line) is a simple moving average of %K:
\[\%D = SMA(\%K, d)\]where d is the d_window.
Traditional interpretation: - %K or %D > 80: Overbought territory (potential sell signal) - %K or %D < 20: Oversold territory (potential buy signal) - %K crossing above %D: Bullish signal - %K crossing below %D: Bearish signal
Key characteristics: - Range: 0 to 100 (bounded oscillator) - %K is more sensitive and reacts faster than %D - Works best in ranging/sideways markets - Divergence between stochastic and price can signal reversals
Examples
Calculate the Stochastic Oscillator on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115, 114, 116], ... 'Low': [100, 102, 101, 103, 105, 104, 106], ... 'Close': [105, 108, 106, 110, 112, 109, 113] ... }) >>> stoch = df.rhoa.indicators.stochastic(k_window=5, d_window=3) >>> print(stoch.columns.tolist()) ['%K', '%D']
Generate crossover signals:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 53, 55, 54, 56, 55, 57, 56], ... 'Low': [48, 49, 51, 50, 52, 51, 53, 52, 54, 53], ... 'Close': [49, 51, 53, 52, 54, 53, 55, 54, 56, 55] ... }) >>> stoch = df.rhoa.indicators.stochastic(k_window=5) >>> buy = (stoch['%K'] > stoch['%D']) & (stoch['%K'].shift(1) <= stoch['%D'].shift(1))
- williams_r(close=None, high=None, low=None, window_size=14, min_periods=None, center=False, **kwargs)[source]
Calculate Williams %R for momentum and overbought/oversold analysis.
Williams %R is a momentum indicator developed by Larry Williams that measures overbought and oversold levels on a scale from -100 to 0. It is the inverse of the Fast Stochastic Oscillator and reflects the level of the close relative to the highest high over the lookback period. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 14) – Number of periods for Williams %R calculation.
min_periods (int, optional) – Minimum observations in window required to have a value.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing Williams %R values ranging from -100 to 0.
- Return type:
See also
stochasticStochastic Oscillator, closely related indicator
rsiRelative Strength Index for momentum
cciCommodity Channel Index for momentum
Notes
Williams %R is calculated as:
\[\%R = -100 \times \frac{H_n - C_t}{H_n - L_n}\]where \(C_t\) is the current close, \(H_n\) is the highest high over the window_size periods, and \(L_n\) is the lowest low over the window_size periods.
Williams %R is mathematically related to the Stochastic Oscillator:
\[\%R = \%K - 100\]Traditional interpretation: - %R between -20 and 0: Overbought (potential sell signal) - %R between -100 and -80: Oversold (potential buy signal) - %R = 0: Close equals the highest high of the period - %R = -100: Close equals the lowest low of the period
Key characteristics: - Range: -100 to 0 (bounded oscillator, negative scale) - Leading indicator: can signal reversals before price - More responsive than RSI to short-term price changes - Works best in ranging markets; use with trend filters
Examples
Calculate 14-period Williams %R:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 111, 113, 115, 114, 116], ... 'Low': [100, 102, 101, 103, 105, 104, 106], ... 'Close': [105, 108, 106, 110, 112, 109, 113] ... }) >>> wr = df.rhoa.indicators.williams_r(window_size=5)
Identify overbought and oversold conditions:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 53, 55, 54, 56, 55, 57, 56], ... 'Low': [48, 49, 51, 50, 52, 51, 53, 52, 54, 53], ... 'Close': [49, 51, 53, 52, 54, 53, 55, 54, 56, 55] ... }) >>> wr = df.rhoa.indicators.williams_r(window_size=5) >>> overbought = wr > -20 >>> oversold = wr < -80
- adx(close=None, high=None, low=None, window_size=14, min_periods=None, **kwargs)[source]
Calculate the Average Directional Index (ADX) for trend strength analysis.
ADX is a trend strength indicator developed by J. Welles Wilder Jr. that quantifies the strength of a trend regardless of its direction. It combines the Plus Directional Indicator (+DI) and Minus Directional Indicator (-DI) to measure how strongly price is moving in one direction. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
window_size (int, default 14) – Number of periods for ADX calculation.
min_periods (int, optional) – Minimum observations in window required to have a value.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A DataFrame with ‘ADX’, ‘+DI’, and ‘-DI’ columns.
- Return type:
See also
atrAverage True Range, used internally by ADX
rsiRelative Strength Index for momentum
parabolic_sarParabolic SAR for trend following
Notes
The calculation involves several steps:
Directional Movement (DM):
\[\begin{split}+DM_t = \begin{cases} H_t - H_{t-1} & \text{if } H_t - H_{t-1} > L_{t-1} - L_t \text{ and } H_t - H_{t-1} > 0 \\ 0 & \text{otherwise} \end{cases}\end{split}\]\[\begin{split}-DM_t = \begin{cases} L_{t-1} - L_t & \text{if } L_{t-1} - L_t > H_t - H_{t-1} \text{ and } L_{t-1} - L_t > 0 \\ 0 & \text{otherwise} \end{cases}\end{split}\]Directional Indicators (DI):
\[+DI = 100 \times \frac{EMA(+DM, n)}{EMA(TR, n)}\]\[-DI = 100 \times \frac{EMA(-DM, n)}{EMA(TR, n)}\]Directional Index (DX) and ADX:
\[DX = 100 \times \frac{|{+DI} - {-DI}|}{+DI + {-DI}}\]\[ADX = EMA(DX, n)\]Traditional interpretation: - ADX > 25: Strong trend (consider trend-following strategies) - ADX < 20: Weak trend or ranging market (consider oscillator strategies) - +DI > -DI: Uptrend (bullish) - -DI > +DI: Downtrend (bearish) - +DI crossing above -DI: Bullish crossover signal - -DI crossing above +DI: Bearish crossover signal
Key characteristics: - ADX measures trend strength, not direction - Rising ADX = strengthening trend; falling ADX = weakening trend - ADX is a lagging indicator due to smoothing
References
Examples
Calculate 14-period ADX on OHLC data:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 114, 113, 115, 117, 116], ... 'Low': [100, 102, 104, 103, 105, 107, 106], ... 'Close': [105, 108, 110, 109, 112, 114, 113] ... }) >>> result = df.rhoa.indicators.adx(window_size=5) >>> print(result.columns.tolist()) ['ADX', '+DI', '-DI']
Identify strong trends and crossover signals:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 56, 58, 57, 55, 53, 51, 49], ... 'Low': [48, 49, 51, 53, 55, 54, 52, 50, 48, 46], ... 'Close': [49, 51, 53, 55, 57, 56, 54, 52, 50, 48] ... }) >>> result = df.rhoa.indicators.adx(window_size=5) >>> strong_trend = result['ADX'] > 25 >>> bullish = result['+DI'] > result['-DI']
- parabolic_sar(close=None, high=None, low=None, af_start=0.02, af_increment=0.02, af_maximum=0.2)[source]
Calculate the Parabolic Stop and Reverse (SAR) for trend following.
Parabolic SAR is a trend-following indicator developed by J. Welles Wilder Jr. that provides potential entry and exit points. It appears as a series of dots placed above or below the price, indicating bearish or bullish conditions respectively. The “parabolic” name comes from the parabola-shaped curve the dots form as a trend develops. Auto-detects Close, High, and Low columns from the DataFrame. Pass explicit Series to override auto-detection.
- Parameters:
close (pandas.Series, optional) – Close prices. Auto-detected from DataFrame if not provided.
high (pandas.Series, optional) – High prices. Auto-detected from DataFrame if not provided.
low (pandas.Series, optional) – Low prices. Auto-detected from DataFrame if not provided.
af_start (float, default 0.02) – Initial acceleration factor.
af_increment (float, default 0.02) – Increment added to acceleration factor when a new extreme point is reached.
af_maximum (float, default 0.2) – Maximum acceleration factor value.
- Returns:
A Series containing Parabolic SAR values.
- Return type:
See also
Notes
The Parabolic SAR is calculated iteratively:
\[SAR_{t+1} = SAR_t + AF \times (EP - SAR_t)\]where: - \(SAR_t\) is the current SAR value - \(AF\) is the acceleration factor, starting at af_start and
increasing by af_increment each time a new extreme point is made, up to af_maximum
\(EP\) is the extreme point (highest high in uptrend, lowest low in downtrend)
Trend reversal occurs when price crosses the SAR value: - In an uptrend, if the low touches or falls below SAR, the trend
reverses to downtrend
In a downtrend, if the high touches or rises above SAR, the trend reverses to uptrend
Upon reversal, the SAR is set to the previous extreme point and the acceleration factor resets to af_start.
Key characteristics: - SAR below price = uptrend (bullish) - SAR above price = downtrend (bearish) - SAR accelerates toward price as a trend develops - Works best in trending markets; can whipsaw in sideways markets
Common applications: - Setting trailing stop-loss orders - Determining trend direction - Identifying potential reversal points - Combining with ADX to filter for strong trends
References
Examples
Calculate Parabolic SAR with default parameters:
>>> import pandas as pd >>> import rhoa >>> df = pd.DataFrame({ ... 'High': [110, 112, 114, 113, 115, 117, 116], ... 'Low': [100, 102, 104, 103, 105, 107, 106], ... 'Close': [105, 108, 110, 109, 112, 114, 113] ... }) >>> sar = df.rhoa.indicators.parabolic_sar()
Use SAR to determine trend direction:
>>> df = pd.DataFrame({ ... 'High': [50, 52, 54, 53, 55, 54, 56, 55, 57, 56], ... 'Low': [48, 49, 51, 50, 52, 51, 53, 52, 54, 53], ... 'Close': [49, 51, 53, 52, 54, 53, 55, 54, 56, 55] ... }) >>> sar = df.rhoa.indicators.parabolic_sar(af_start=0.02, af_maximum=0.2) >>> uptrend = df['Close'] > sar >>> downtrend = df['Close'] < sar
Function Reference
Moving Averages
- sma(self, window_size=20, min_periods=None, center=False, **kwargs)
Calculate the Simple Moving Average (SMA) over a specified window.
The SMA is a commonly used technical indicator in financial and time series analysis that calculates the arithmetic mean of prices over a defined number of periods. It smooths out price data to identify trends by reducing noise from short-term fluctuations.
- Parameters:
window_size (int, default 20) – The size of the moving window, representing the number of periods over which to calculate the average.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to window_size.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A Series containing the calculated SMA values with the same index as the input series.
- Return type:
See also
ewmaExponential Weighted Moving Average for trend analysis
bollinger_bandsUses SMA as the middle band
macdUses exponential moving averages
Notes
The Simple Moving Average is calculated as:
\[SMA_t = \frac{1}{n} \sum_{i=0}^{n-1} P_{t-i}\]where \(P_t\) is the price at time t and n is the window_size.
The first window_size - 1 values will be NaN unless min_periods is set to a lower value. SMA gives equal weight to all values in the window, which can make it slower to respond to recent price changes compared to exponential moving averages.
SMA is commonly used for: - Identifying support and resistance levels - Generating crossover trading signals (e.g., golden cross, death cross) - Smoothing price data for trend identification
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.sma(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 20-period Simple Moving Average:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106]) >>> sma = prices.rhoa.indicators.sma(window_size=5) >>> print(sma.iloc[4]) # First valid SMA value 102.2
Generate trading signals using SMA crossover:
>>> prices = pd.Series([100, 102, 104, 106, 108, 107, 105, 103, 101]) >>> sma_short = prices.rhoa.indicators.sma(window_size=3) >>> sma_long = prices.rhoa.indicators.sma(window_size=5) >>> buy_signal = (sma_short > sma_long) & (sma_short.shift(1) <= sma_long.shift(1))
- ewma(self, window_size=20, adjust=False, min_periods=None, **kwargs)
Calculate the Exponential Weighted Moving Average (EWMA) of the series.
The EWMA is a type of infinite impulse response filter that applies weighting factors which decrease exponentially. Unlike simple moving averages, EWMA gives more weight to recent observations, making it more responsive to recent price changes while still providing smoothing.
- Parameters:
window_size (int, default 20) – The span of the exponential moving average. Determines the level of smoothing, where larger values result in smoother trends and slower responsiveness to changes in the data.
adjust (bool, default False) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights to account for the imbalance in the beginning periods.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the calculated EWMA values with the same index as the input series.
- Return type:
See also
Notes
The Exponential Weighted Moving Average is calculated using:
\[EWMA_t = \alpha \cdot P_t + (1 - \alpha) \cdot EWMA_{t-1}\]where \(\alpha = \frac{2}{span + 1}\) and span is the window_size.
Key characteristics: - More weight to recent prices: reacts faster to recent changes - Smoother than price but more responsive than SMA - All historical data has some influence (infinite impulse response) - No lookback period required (unlike SMA)
The adjust parameter affects the calculation in the initial periods: - adjust=True: Uses normalized weights (standard EWMA definition) - adjust=False: Uses recursive formula (more common in trading)
EWMA is commonly used for: - Trend identification and confirmation - Support and resistance levels that adapt to volatility - Component of MACD and other composite indicators
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewma(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 20-period Exponential Weighted Moving Average:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106, 108]) >>> ewma = prices.rhoa.indicators.ewma(window_size=5) >>> print(f"Latest EWMA: {ewma.iloc[-1]:.2f}") Latest EWMA: 105.45
Compare EWMA with different window sizes:
>>> ewma_fast = prices.rhoa.indicators.ewma(window_size=5) >>> ewma_slow = prices.rhoa.indicators.ewma(window_size=20) >>> crossover = (ewma_fast > ewma_slow) & (ewma_fast.shift(1) <= ewma_slow.shift(1))
- ewmv(self, window_size=20, adjust=True, min_periods=None, **kwargs)
Calculate the exponentially weighted moving variance (EWMV) of a series.
This method computes the variance of a series by applying exponential weighting to give more importance to recent observations. EWMV is useful for measuring volatility that adapts more quickly to recent price changes compared to standard rolling variance.
- Parameters:
window_size (int, default 20) – The span of the exponential window. Determines the level of smoothing applied to the variance calculation. Larger values result in smoother variance estimates.
adjust (bool, default True) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the exponentially weighted moving variance values with the same index as the input series.
- Return type:
See also
ewmstdExponential Weighted Moving Standard Deviation
ewmaExponential Weighted Moving Average
bollinger_bandsUses standard deviation for band calculation
Notes
The exponentially weighted moving variance uses exponential smoothing to calculate variance with the formula:
\[EWMV_t = \alpha \sum_{i=0}^{t} (1-\alpha)^i (P_{t-i} - EWMA_t)^2\]where \(\alpha = \frac{2}{span + 1}\) and span is the window_size.
Key properties: - Always non-negative (variance cannot be negative) - More responsive to recent volatility changes than rolling variance - Relationship: \(EWMV = EWMSTD^2\) - Units are squared (e.g., squared dollars for price data)
Higher variance values indicate increased volatility and risk. EWMV is commonly used for: - Volatility estimation in risk management - Detecting regime changes in market conditions - Building adaptive trading strategies - Calculating value-at-risk (VaR) metrics
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewmv(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate exponentially weighted moving variance:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104]) >>> ewmv = prices.rhoa.indicators.ewmv(window_size=5) >>> print(f"Latest variance: {ewmv.iloc[-1]:.2f}") Latest variance: 6.24
Detect periods of high volatility:
>>> prices = pd.Series([100, 102, 101, 103, 105, 104, 110, 95, 105, 100]) >>> ewmv = prices.rhoa.indicators.ewmv(window_size=5) >>> high_volatility = ewmv > ewmv.rolling(20).mean() * 1.5
- ewmstd(self, window_size=20, adjust=True, min_periods=None, **kwargs)
Calculate the exponentially weighted moving standard deviation (EWMSTD).
EWMSTD is a statistical measure that weights recent data points more heavily to provide a smoothed calculation of the moving standard deviation. This makes it more responsive to recent volatility changes compared to traditional rolling standard deviation, while maintaining smoothness.
- Parameters:
window_size (int, default 20) – The span or window size for the exponentially weighted moving calculation. Smaller spans apply heavier weighting to more recent data points and react faster to changes, while larger spans provide smoother results.
adjust (bool, default True) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to 0.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing the exponentially weighted moving standard deviation values with the same index as the input series.
- Return type:
See also
ewmvExponential Weighted Moving Variance
ewmaExponential Weighted Moving Average
bollinger_bandsUses standard deviation for volatility bands
atrAverage True Range for volatility measurement
Notes
The exponentially weighted moving standard deviation is the square root of the exponentially weighted moving variance:
\[EWMSTD_t = \sqrt{EWMV_t}\]where \(EWMV_t\) is calculated with exponential weights.
The relationship \(EWMSTD^2 = EWMV\) always holds.
Key characteristics: - Always non-negative (standard deviation cannot be negative) - Same units as the original series (unlike variance) - More responsive to recent volatility than rolling standard deviation - Commonly used as a volatility proxy in trading
EWMSTD is commonly used for: - Volatility-based position sizing - Risk management and stop-loss placement - Adaptive trading strategies that respond to volatility - Bollinger Bands and other volatility indicators - Normalized price movements (z-scores)
Higher values indicate increased volatility and uncertainty.
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.ewmstd(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate exponentially weighted moving standard deviation:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104]) >>> ewmstd = prices.rhoa.indicators.ewmstd(window_size=5) >>> print(f"Latest volatility: {ewmstd.iloc[-1]:.2f}") Latest volatility: 2.50
Use EWMSTD for volatility-adjusted position sizing:
>>> prices = pd.Series([100, 102, 104, 106, 108, 110, 112]) >>> volatility = prices.rhoa.indicators.ewmstd(window_size=10) >>> position_size = 1000 / volatility # Risk-adjusted sizing
Momentum Oscillators
- rsi(self, window_size=14, edge_case_value=100.0, **kwargs)
Calculate the Relative Strength Index (RSI) for momentum analysis.
RSI is a momentum oscillator that measures the speed and magnitude of price changes on a scale of 0 to 100. Developed by J. Welles Wilder Jr., it helps identify overbought and oversold conditions, as well as potential trend reversals. RSI is one of the most widely used technical indicators in trading.
- Parameters:
window_size (int, default 14) – The size of the rolling window used to calculate the exponential moving averages of gains and losses. Traditional value is 14 periods as recommended by Wilder.
edge_case_value (float, default 100.0) – The RSI value to use when avg_loss == 0 (no losses occurred in the period). Common values are 100.0 (infinite RS, default), 50.0 (neutral), or numpy.nan.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A Series containing RSI values between 0 and 100 with the same index as the input series.
- Return type:
See also
stochasticSimilar momentum oscillator
cciCommodity Channel Index for momentum
williams_rWilliams %R momentum indicator
macdMoving Average Convergence Divergence
Notes
The Relative Strength Index is calculated using:
\[RSI = 100 - \frac{100}{1 + RS}\]where \(RS = \frac{EMA(gains)}{EMA(losses)}\) and EMA is the exponential moving average over the specified window_size.
Traditional interpretation levels: - RSI > 70: Overbought condition (potential sell signal) - RSI < 30: Oversold condition (potential buy signal) - RSI = 50: Neutral momentum (balance between bulls and bears)
Key characteristics: - Range: 0 to 100 (bounded oscillator) - Mean-reverting: tends to oscillate around 50 - Leading indicator: can signal reversals before price - Works best in ranging markets (less reliable in strong trends)
Advanced RSI techniques: - Divergence: RSI diverging from price can signal reversals - Failure swings: RSI patterns that don’t confirm new price highs/lows - Centerline crossovers: RSI crossing 50 confirms trend direction - Dynamic thresholds: Use 80/20 in strong trends instead of 70/30
The first window_size values will be NaN as the indicator requires sufficient data to calculate the initial exponential moving averages.
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.rsi(window_size=14)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate 14-period RSI and identify trading signals:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110, 109]) >>> rsi = prices.rhoa.indicators.rsi(window_size=14) >>> overbought = rsi > 70 # Potential sell signals >>> oversold = rsi < 30 # Potential buy signals >>> print(f"Latest RSI: {rsi.iloc[-1]:.1f}") Latest RSI: 75.2
Detect RSI divergence for reversal signals:
>>> prices = pd.Series([100, 105, 110, 115, 120, 118, 116, 114]) >>> rsi = prices.rhoa.indicators.rsi() >>> # Bearish divergence: price makes new high but RSI doesn't >>> price_higher = prices > prices.shift(1).rolling(5).max() >>> rsi_lower = rsi < rsi.shift(1).rolling(5).max() >>> divergence = price_higher & rsi_lower
Trend Indicators
- macd(self, short_window=12, long_window=26, signal_window=9, **kwargs)
Calculate the MACD (Moving Average Convergence Divergence) indicator.
MACD is a trend-following momentum indicator that shows the relationship between two exponential moving averages of a security’s price. Developed by Gerald Appel, it consists of three components that together provide insights into trend direction, momentum strength, and potential reversals.
- Parameters:
short_window (int, default 12) – Length of the short-term (fast) EMA window in periods. Smaller values make MACD more responsive to recent price changes.
long_window (int, default 26) – Length of the long-term (slow) EMA window in periods. Larger values provide more smoothing and stability.
signal_window (int, default 9) – Length of the signal line EMA window in periods. This smooths the MACD line to generate trading signals.
**kwargs (dict) – Additional keyword arguments passed to pandas ewm function.
- Returns:
A DataFrame with three columns: - ‘macd’ : The MACD line (short_ema - long_ema) - ‘signal’ : The signal line (EMA of MACD line) - ‘histogram’ : The MACD histogram (macd - signal)
- Return type:
See also
Notes
The MACD indicator components are calculated as:
\[MACD_{line} = EMA_{short} - EMA_{long}\]\[Signal_{line} = EMA_{signal}(MACD_{line})\]\[Histogram = MACD_{line} - Signal_{line}\]Traditional interpretation: - MACD line crosses above signal: Bullish signal (buy) - MACD line crosses below signal: Bearish signal (sell) - Histogram > 0: MACD above signal (bullish momentum) - Histogram < 0: MACD below signal (bearish momentum) - Histogram expanding: Momentum increasing - Histogram contracting: Momentum decreasing
Key characteristics: - Unbounded oscillator (can take any value) - Combines trend-following and momentum aspects - Three signals: crossovers, divergences, and rapid rises/falls - Works best in trending markets
Advanced MACD techniques: - Divergence: MACD diverging from price signals potential reversals - Zero-line crossovers: MACD crossing zero indicates trend change - Histogram analysis: Momentum changes before MACD line crosses - Multiple timeframe confirmation
The standard parameters (12, 26, 9) were optimized for daily charts but can be adjusted for different timeframes or market characteristics.
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.macd()which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate MACD and identify bullish crossover:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110]) >>> macd_data = prices.rhoa.indicators.macd() >>> # Bullish signal: MACD crosses above signal >>> bullish = (macd_data['macd'] > macd_data['signal']) & ... (macd_data['macd'].shift(1) <= macd_data['signal'].shift(1)) >>> print(f"MACD: {macd_data['macd'].iloc[-1]:.3f}") MACD: 0.245
Analyze MACD histogram for momentum changes:
>>> macd_data = prices.rhoa.indicators.macd() >>> histogram = macd_data['histogram'] >>> momentum_increasing = histogram > histogram.shift(1) >>> momentum_peak = (histogram.shift(1) > histogram) & (histogram.shift(1) > histogram.shift(2))
Volatility Indicators
- bollinger_bands(self, window_size=20, num_std=2.0, min_periods=None, center=False, **kwargs)
Calculate Bollinger Bands for volatility and mean reversion analysis.
Bollinger Bands consist of three lines: an upper band, middle band (SMA), and lower band. Developed by John Bollinger, the bands expand and contract based on market volatility, providing insights into potential overbought/ oversold conditions, volatility patterns, and mean reversion opportunities.
- Parameters:
window_size (int, default 20) – The size of the rolling window used for computing the moving average and standard deviation. Standard setting is 20 periods.
num_std (float, default 2.0) – The number of standard deviations to add/subtract from the moving average to calculate the upper and lower bands. Standard setting is 2.0.
min_periods (int, optional) – Minimum number of observations in window required to have a value. If None, defaults to window_size.
center (bool, default False) – Whether to set the labels at the center of the window.
**kwargs (dict) – Additional keyword arguments passed to pandas rolling function.
- Returns:
A DataFrame with three columns: - ‘upper_band’ : Upper Bollinger Band (middle + num_std * std) - ‘middle_band’ : Middle band (SMA of the series) - ‘lower_band’ : Lower Bollinger Band (middle - num_std * std)
- Return type:
See also
Notes
Bollinger Bands are calculated using:
\[Middle_{band} = SMA(price, window)\]\[Upper_{band} = Middle_{band} + (num\_std \times \sigma)\]\[Lower_{band} = Middle_{band} - (num\_std \times \sigma)\]where \(\sigma\) is the standard deviation over the window.
Traditional interpretation: - Price touching upper band: Potentially overbought (high relative price) - Price touching lower band: Potentially oversold (low relative price) - Price between bands: Normal trading range - Band width: Measure of volatility
Key characteristics: - Approximately 95% of price action occurs within 2 standard deviations - Bands are dynamic support/resistance levels - Band width reflects market volatility - Works as both a trend and volatility indicator
Common Bollinger Band strategies: - Squeeze: Narrow bands indicate low volatility, often precedes breakout - Expansion: Wide bands indicate high volatility - Band walk: Price riding upper/lower band indicates strong trend - Bollinger Bounce: Mean reversion trades off band touches - %B indicator: (price - lower) / (upper - lower) shows relative position
Advanced techniques: - Double tops/bottoms at bands for reversal signals - M-tops and W-bottoms for patterns - Band width as volatility indicator - Combination with other indicators for confirmation
References
Tip
Also available via DataFrame accessor:
df.rhoa.indicators.bollinger_bands(window_size=20)which defaults to the Close column. SeeDataFrameIndicators.Examples
Calculate Bollinger Bands and identify squeeze conditions:
>>> import pandas as pd >>> import rhoa >>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107]) >>> bb = prices.rhoa.indicators.bollinger_bands(window_size=5, num_std=2.0) >>> # Band width indicates volatility >>> width = bb['upper_band'] - bb['lower_band'] >>> squeeze = width < width.rolling(10).mean() * 0.8 # Low volatility >>> print(f"Upper: {bb['upper_band'].iloc[-1]:.2f}") Upper: 109.45
Calculate %B indicator for position within bands:
>>> bb = prices.rhoa.indicators.bollinger_bands() >>> percent_b = (prices - bb['lower_band']) / (bb['upper_band'] - bb['lower_band']) >>> overbought = percent_b > 1.0 # Price above upper band >>> oversold = percent_b < 0.0 # Price below lower band