rhoa.indicators module

class indicators

Bases: object

__init__(series)

Parameters:

series (Series)

Return type:

None

sma(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 average value over a defined number of periods.

Parameters:

• window_size (int, optional) – The size of the moving window, representing the number of periods over which to calculate the average. Defaults to 20.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A pandas Series containing the calculated SMA values.

Return type:

pandas.Series

Example

Calculate 20-period Simple Moving Average:

>>> import pandas as pd
>>> import rhoa
>>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106])
>>> sma = prices.indicators.sma(window_size=5)
>>> print(sma.iloc[4])  # First valid SMA value
102.2

Note

The first window_size - 1 values will be NaN since there aren’t enough observations to calculate the average.

ewma(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. This method is commonly used in financial time series to smooth data and compute trends. Unlike simple moving averages, EWMA gives more weight to recent observations.

Parameters:

• window_size (int, optional) – 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. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to False.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the calculated EWMA values.

Return type:

pandas.Series

Example

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.indicators.ewma(window_size=5)
>>> print(f"Latest EWMA: {ewma.iloc[-1]:.2f}")
Latest EWMA: 105.45

Note

EWMA responds more quickly to recent price changes compared to SMA, making it useful for trend following strategies.

ewmv(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. The window size parameter determines the span of the exponentially weighted period. EWMV is useful for measuring volatility that adapts more quickly to recent price changes.

Parameters:

• window_size (int, optional) – The span of the exponential window. Determines the level of smoothing applied to the variance calculation. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to True.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the exponentially weighted moving

variance of the input series.

Return type:

pandas.Series

Example

Calculate exponentially weighted moving variance:

>>> import pandas as pd
>>> import rhoa
>>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104])
>>> ewmv = prices.indicators.ewmv(window_size=5)
>>> print(f"Latest variance: {ewmv.iloc[-1]:.2f}")
Latest variance: 6.24

Note

Higher variance values indicate increased volatility in the price series. The variance is always non-negative.

ewmstd(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.

Parameters:

• window_size (int, optional) – The span or window size for the exponentially weighted moving calculation. Smaller spans apply heavier weighting to more recent data points, while larger spans provide smoother results. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to True.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the exponentially weighted moving

standard deviation values.

Return type:

pandas.Series

Example

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.indicators.ewmstd(window_size=5)
>>> print(f"Latest volatility: {ewmstd.iloc[-1]:.2f}")
Latest volatility: 2.50

Note

The relationship EWMSTD² = EWMV holds. This indicator is commonly used for volatility-based trading strategies and risk management.

rsi(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 change of price movements on a scale of 0 to 100. It helps identify overbought (typically >70) and oversold (typically <30) market conditions. RSI is one of the most widely used technical indicators in trading.

Parameters:

• window_size (int, optional) – The size of the rolling window used to calculate the moving averages of gains and losses. Traditional value is 14. Defaults to 14.

• edge_case_value (float, optional) – The RSI value to use when avg_loss == 0 (no losses occurred). Common values: 100.0 (infinite RS, default), 50.0 (neutral), or float(‘nan’). Defaults to 100.0.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing RSI values between 0 and 100.

Return type:

pandas.Series

Example

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.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

Note

• RSI > 70: Generally considered overbought (potential sell signal)

• RSI < 30: Generally considered oversold (potential buy signal)

• RSI around 50: Neutral momentum

macd(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 moving averages of a security’s price. It consists of three components: the MACD line, signal line, and histogram, which together provide insights into trend direction and momentum changes.

The MACD line is the difference between the short-term and long-term EMAs. The signal line is an EMA of the MACD line. The histogram shows the difference between MACD and signal lines.

Parameters:

• short_window (int, optional) – Length of the short-term EMA window. Defaults to 12.

• long_window (int, optional) – Length of the long-term EMA window. Defaults to 26.

• signal_window (int, optional) – Length of the signal EMA window. Defaults to 9.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A DataFrame with columns ‘macd’, ‘signal’, and ‘histogram’.

Return type:

pandas.DataFrame

Example

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.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

Note

• Bullish signal: MACD line crosses above signal line

• Bearish signal: MACD line crosses below signal line

• Histogram > 0: MACD above signal (bullish momentum)

• Histogram < 0: MACD below signal (bearish momentum)

bollinger_bands(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. The bands expand and contract based on market volatility, providing insights into potential overbought/oversold conditions and price volatility patterns.

Parameters:

• window_size (int, optional) – The size of the rolling window used for computing the moving average and standard deviation. Defaults to 20.

• num_std (float, optional) – The number of standard deviations to add/subtract from the moving average to calculate the upper and lower bands. Defaults to 2.0.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A DataFrame with columns ‘upper_band’, ‘middle_band’,

and ‘lower_band’.

Return type:

pandas.DataFrame

Example

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.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

Note

• Price touching upper band: Potentially overbought

• Price touching lower band: Potentially oversold

• Narrow bands: Low volatility (squeeze)

• Wide bands: High volatility (expansion)

atr(high, low, window_size=14, min_periods=None, center=False, **kwargs)

Calculate the Average True Range (ATR) for volatility measurement.

ATR measures market volatility by calculating the average of true ranges over a specified period. True range is the maximum of: (high - low), (high - previous close), or (low - previous close). ATR is widely used for position sizing and stop-loss placement.

Parameters:

• high (pandas.Series) – A Series representing the high prices.

• low (pandas.Series) – A Series representing the low prices.

• window_size (int, optional) – Length of the rolling window for calculating the average true range. Defaults to 14.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series containing the calculated ATR values.

Return type:

pandas.Series

Example

Calculate ATR for position sizing:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105])
>>> atr = close.indicators.atr(high, low, window_size=5)
>>> # Use ATR for stop-loss: 2 * ATR below entry
>>> stop_distance = 2 * atr.iloc[-1]
>>> print(f"ATR: {atr.iloc[-1]:.2f}, Stop distance: {stop_distance:.2f}")
ATR: 1.80, Stop distance: 3.60

Note

Higher ATR values indicate higher volatility. ATR is commonly used for setting stop-losses and position sizing in trading strategies.

cci(high, low, window_size=20, min_periods=None, center=False, **kwargs)

Calculate the Commodity Channel Index (CCI) for momentum analysis.

CCI is a momentum-based oscillator that measures the variation of a security’s price from its statistical mean. It oscillates above and below zero, with readings above +100 indicating overbought conditions and readings below -100 indicating oversold conditions.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for calculating the CCI. Defaults to 20.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series representing the calculated CCI values.

Return type:

pandas.Series

Example

Calculate CCI and identify trading signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> cci = close.indicators.cci(high, low, window_size=5)
>>> overbought = cci > 100   # Potential sell signals
>>> oversold = cci < -100    # Potential buy signals
>>> print(f"Latest CCI: {cci.iloc[-1]:.1f}")
Latest CCI: 85.2

Note

• CCI > +100: Overbought condition (potential sell signal)

• CCI < -100: Oversold condition (potential buy signal)

• CCI around 0: Normal trading range

stochastic(high, low, k_window=14, d_window=3, min_periods=None, center=False, **kwargs)

Calculate the Stochastic Oscillator (%K and %D) for momentum analysis.

The Stochastic Oscillator compares a closing price to its price range over a given time period. It generates values between 0 and 100, where values above 80 typically indicate overbought conditions and values below 20 indicate oversold conditions.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• k_window (int, optional) – Number of periods for %K calculation. Defaults to 14.

• d_window (int, optional) – Number of periods for %D calculation (SMA of %K). Defaults to 3.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A DataFrame with ‘%K’ and ‘%D’ columns representing

the stochastic values.

Return type:

pandas.DataFrame

Example

Calculate Stochastic Oscillator and identify signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> stoch = close.indicators.stochastic(high, low, k_window=5, d_window=3)
>>> overbought = stoch['%K'] > 80  # Potential sell signals
>>> oversold = stoch['%K'] < 20   # Potential buy signals
>>> print(f"%K: {stoch['%K'].iloc[-1]:.1f}, %D: {stoch['%D'].iloc[-1]:.1f}")
%K: 75.0, %D: 72.3

Note

• %K > 80: Overbought (potential sell signal)

• %K < 20: Oversold (potential buy signal)

• %K crossing above %D: Bullish signal

• %K crossing below %D: Bearish signal

williams_r(high, low, window_size=14, min_periods=None, center=False, **kwargs)

Calculate Williams %R for momentum and overbought/oversold analysis.

Williams %R is a momentum indicator that measures overbought and oversold levels. It oscillates between -100 and 0, with readings above -20 indicating overbought conditions and readings below -80 indicating oversold conditions. It’s essentially an inverted Stochastic Oscillator.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for Williams %R calculation. Defaults to 14.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series representing Williams %R values (-100 to 0).

Return type:

pandas.Series

Example

Calculate Williams %R and identify trading signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> wr = close.indicators.williams_r(high, low, window_size=5)
>>> overbought = wr > -20  # Potential sell signals
>>> oversold = wr < -80   # Potential buy signals
>>> print(f"Williams %R: {wr.iloc[-1]:.1f}")
Williams %R: -25.0

Note

• Williams %R > -20: Overbought (potential sell signal)

• Williams %R < -80: Oversold (potential buy signal)

• Values closer to 0: Stronger momentum

• Values closer to -100: Weaker momentum

adx(high, low, window_size=14, min_periods=None, **kwargs)

Calculate the Average Directional Index (ADX) for trend strength analysis.

ADX is a non-directional indicator that quantifies trend strength regardless of direction. It ranges from 0 to 100, with higher values indicating stronger trends. The calculation includes +DI and -DI (Directional Indicators) that measure upward and downward price movement strength.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for ADX calculation. Defaults to 14.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A DataFrame with ‘ADX’, ‘+DI’, and ‘-DI’ columns.

Return type:

pandas.DataFrame

Example

Calculate ADX and assess trend strength:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 104, 106, 108, 110, 112, 114, 116])
>>> high = pd.Series([101, 103, 105, 107, 109, 111, 113, 115, 117])
>>> low = pd.Series([99, 101, 103, 105, 107, 109, 111, 113, 115])
>>> adx_data = close.indicators.adx(high, low, window_size=5)
>>> strong_trend = adx_data['ADX'] > 25  # Strong trend identification
>>> bullish = adx_data['+DI'] > adx_data['-DI']  # Uptrend
>>> print(f"ADX: {adx_data['ADX'].iloc[-1]:.1f}")
ADX: 45.2

Note

• ADX > 25: Strong trend (regardless of direction)

• ADX < 20: Weak trend or sideways market

• +DI > -DI: Uptrend strength

• -DI > +DI: Downtrend strength

parabolic_sar(high, low, af_start=0.02, af_increment=0.02, af_maximum=0.2)

Calculate the Parabolic Stop and Reverse (SAR) for trend following.

Parabolic SAR is a trend-following indicator that provides potential reversal points and trailing stop levels. It appears as dots above or below price: dots below indicate uptrends, dots above indicate downtrends. The indicator uses an acceleration factor that increases over time for sensitivity.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• af_start (float, optional) – Initial acceleration factor. Defaults to 0.02.

• af_increment (float, optional) – Increment added to acceleration factor when new extreme is reached. Defaults to 0.02.

• af_maximum (float, optional) – Maximum acceleration factor value. Defaults to 0.2.

Returns:

A Series representing Parabolic SAR values.

Return type:

pandas.Series

Example

Calculate Parabolic SAR for trend identification and stops:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110])
>>> high = pd.Series([101, 103, 105, 104, 106, 108, 107, 109, 111])
>>> low = pd.Series([99, 101, 103, 102, 104, 106, 105, 107, 109])
>>> sar = close.indicators.parabolic_sar(high, low)
>>> uptrend = close > sar    # Price above SAR = uptrend
>>> downtrend = close < sar  # Price below SAR = downtrend
>>> print(f"Latest SAR: {sar.iloc[-1]:.2f}")
Latest SAR: 99.45

Note

• Price above SAR: Uptrend (SAR acts as support)

• Price below SAR: Downtrend (SAR acts as resistance)

• SAR flip: Potential trend reversal signal

• Use SAR as trailing stop-loss levels

The indicators module provides technical analysis indicators through pandas Series accessor.

indicators Class

class indicators

Bases: object

__init__(series)

Parameters:

series (Series)

Return type:

None

sma(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 average value over a defined number of periods.

Parameters:

• window_size (int, optional) – The size of the moving window, representing the number of periods over which to calculate the average. Defaults to 20.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A pandas Series containing the calculated SMA values.

Return type:

pandas.Series

Example

Calculate 20-period Simple Moving Average:

>>> import pandas as pd
>>> import rhoa
>>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106])
>>> sma = prices.indicators.sma(window_size=5)
>>> print(sma.iloc[4])  # First valid SMA value
102.2

Note

The first window_size - 1 values will be NaN since there aren’t enough observations to calculate the average.

ewma(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. This method is commonly used in financial time series to smooth data and compute trends. Unlike simple moving averages, EWMA gives more weight to recent observations.

Parameters:

• window_size (int, optional) – 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. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to False.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the calculated EWMA values.

Return type:

pandas.Series

Example

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.indicators.ewma(window_size=5)
>>> print(f"Latest EWMA: {ewma.iloc[-1]:.2f}")
Latest EWMA: 105.45

Note

EWMA responds more quickly to recent price changes compared to SMA, making it useful for trend following strategies.

ewmv(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. The window size parameter determines the span of the exponentially weighted period. EWMV is useful for measuring volatility that adapts more quickly to recent price changes.

Parameters:

• window_size (int, optional) – The span of the exponential window. Determines the level of smoothing applied to the variance calculation. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to True.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the exponentially weighted moving

variance of the input series.

Return type:

pandas.Series

Example

Calculate exponentially weighted moving variance:

>>> import pandas as pd
>>> import rhoa
>>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104])
>>> ewmv = prices.indicators.ewmv(window_size=5)
>>> print(f"Latest variance: {ewmv.iloc[-1]:.2f}")
Latest variance: 6.24

Note

Higher variance values indicate increased volatility in the price series. The variance is always non-negative.

ewmstd(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.

Parameters:

• window_size (int, optional) – The span or window size for the exponentially weighted moving calculation. Smaller spans apply heavier weighting to more recent data points, while larger spans provide smoother results. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to True.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the exponentially weighted moving

standard deviation values.

Return type:

pandas.Series

Example

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.indicators.ewmstd(window_size=5)
>>> print(f"Latest volatility: {ewmstd.iloc[-1]:.2f}")
Latest volatility: 2.50

Note

The relationship EWMSTD² = EWMV holds. This indicator is commonly used for volatility-based trading strategies and risk management.

rsi(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 change of price movements on a scale of 0 to 100. It helps identify overbought (typically >70) and oversold (typically <30) market conditions. RSI is one of the most widely used technical indicators in trading.

Parameters:

• window_size (int, optional) – The size of the rolling window used to calculate the moving averages of gains and losses. Traditional value is 14. Defaults to 14.

• edge_case_value (float, optional) – The RSI value to use when avg_loss == 0 (no losses occurred). Common values: 100.0 (infinite RS, default), 50.0 (neutral), or float(‘nan’). Defaults to 100.0.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing RSI values between 0 and 100.

Return type:

pandas.Series

Example

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.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

Note

• RSI > 70: Generally considered overbought (potential sell signal)

• RSI < 30: Generally considered oversold (potential buy signal)

• RSI around 50: Neutral momentum

macd(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 moving averages of a security’s price. It consists of three components: the MACD line, signal line, and histogram, which together provide insights into trend direction and momentum changes.

The MACD line is the difference between the short-term and long-term EMAs. The signal line is an EMA of the MACD line. The histogram shows the difference between MACD and signal lines.

Parameters:

• short_window (int, optional) – Length of the short-term EMA window. Defaults to 12.

• long_window (int, optional) – Length of the long-term EMA window. Defaults to 26.

• signal_window (int, optional) – Length of the signal EMA window. Defaults to 9.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A DataFrame with columns ‘macd’, ‘signal’, and ‘histogram’.

Return type:

pandas.DataFrame

Example

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.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

Note

• Bullish signal: MACD line crosses above signal line

• Bearish signal: MACD line crosses below signal line

• Histogram > 0: MACD above signal (bullish momentum)

• Histogram < 0: MACD below signal (bearish momentum)

bollinger_bands(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. The bands expand and contract based on market volatility, providing insights into potential overbought/oversold conditions and price volatility patterns.

Parameters:

• window_size (int, optional) – The size of the rolling window used for computing the moving average and standard deviation. Defaults to 20.

• num_std (float, optional) – The number of standard deviations to add/subtract from the moving average to calculate the upper and lower bands. Defaults to 2.0.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A DataFrame with columns ‘upper_band’, ‘middle_band’,

and ‘lower_band’.

Return type:

pandas.DataFrame

Example

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.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

Note

• Price touching upper band: Potentially overbought

• Price touching lower band: Potentially oversold

• Narrow bands: Low volatility (squeeze)

• Wide bands: High volatility (expansion)

atr(high, low, window_size=14, min_periods=None, center=False, **kwargs)

Calculate the Average True Range (ATR) for volatility measurement.

ATR measures market volatility by calculating the average of true ranges over a specified period. True range is the maximum of: (high - low), (high - previous close), or (low - previous close). ATR is widely used for position sizing and stop-loss placement.

Parameters:

• high (pandas.Series) – A Series representing the high prices.

• low (pandas.Series) – A Series representing the low prices.

• window_size (int, optional) – Length of the rolling window for calculating the average true range. Defaults to 14.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series containing the calculated ATR values.

Return type:

pandas.Series

Example

Calculate ATR for position sizing:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105])
>>> atr = close.indicators.atr(high, low, window_size=5)
>>> # Use ATR for stop-loss: 2 * ATR below entry
>>> stop_distance = 2 * atr.iloc[-1]
>>> print(f"ATR: {atr.iloc[-1]:.2f}, Stop distance: {stop_distance:.2f}")
ATR: 1.80, Stop distance: 3.60

Note

Higher ATR values indicate higher volatility. ATR is commonly used for setting stop-losses and position sizing in trading strategies.

cci(high, low, window_size=20, min_periods=None, center=False, **kwargs)

Calculate the Commodity Channel Index (CCI) for momentum analysis.

CCI is a momentum-based oscillator that measures the variation of a security’s price from its statistical mean. It oscillates above and below zero, with readings above +100 indicating overbought conditions and readings below -100 indicating oversold conditions.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for calculating the CCI. Defaults to 20.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series representing the calculated CCI values.

Return type:

pandas.Series

Example

Calculate CCI and identify trading signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> cci = close.indicators.cci(high, low, window_size=5)
>>> overbought = cci > 100   # Potential sell signals
>>> oversold = cci < -100    # Potential buy signals
>>> print(f"Latest CCI: {cci.iloc[-1]:.1f}")
Latest CCI: 85.2

Note

• CCI > +100: Overbought condition (potential sell signal)

• CCI < -100: Oversold condition (potential buy signal)

• CCI around 0: Normal trading range

stochastic(high, low, k_window=14, d_window=3, min_periods=None, center=False, **kwargs)

Calculate the Stochastic Oscillator (%K and %D) for momentum analysis.

The Stochastic Oscillator compares a closing price to its price range over a given time period. It generates values between 0 and 100, where values above 80 typically indicate overbought conditions and values below 20 indicate oversold conditions.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• k_window (int, optional) – Number of periods for %K calculation. Defaults to 14.

• d_window (int, optional) – Number of periods for %D calculation (SMA of %K). Defaults to 3.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A DataFrame with ‘%K’ and ‘%D’ columns representing

the stochastic values.

Return type:

pandas.DataFrame

Example

Calculate Stochastic Oscillator and identify signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> stoch = close.indicators.stochastic(high, low, k_window=5, d_window=3)
>>> overbought = stoch['%K'] > 80  # Potential sell signals
>>> oversold = stoch['%K'] < 20   # Potential buy signals
>>> print(f"%K: {stoch['%K'].iloc[-1]:.1f}, %D: {stoch['%D'].iloc[-1]:.1f}")
%K: 75.0, %D: 72.3

Note

• %K > 80: Overbought (potential sell signal)

• %K < 20: Oversold (potential buy signal)

• %K crossing above %D: Bullish signal

• %K crossing below %D: Bearish signal

williams_r(high, low, window_size=14, min_periods=None, center=False, **kwargs)

Calculate Williams %R for momentum and overbought/oversold analysis.

Williams %R is a momentum indicator that measures overbought and oversold levels. It oscillates between -100 and 0, with readings above -20 indicating overbought conditions and readings below -80 indicating oversold conditions. It’s essentially an inverted Stochastic Oscillator.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for Williams %R calculation. Defaults to 14.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series representing Williams %R values (-100 to 0).

Return type:

pandas.Series

Example

Calculate Williams %R and identify trading signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> wr = close.indicators.williams_r(high, low, window_size=5)
>>> overbought = wr > -20  # Potential sell signals
>>> oversold = wr < -80   # Potential buy signals
>>> print(f"Williams %R: {wr.iloc[-1]:.1f}")
Williams %R: -25.0

Note

• Williams %R > -20: Overbought (potential sell signal)

• Williams %R < -80: Oversold (potential buy signal)

• Values closer to 0: Stronger momentum

• Values closer to -100: Weaker momentum

adx(high, low, window_size=14, min_periods=None, **kwargs)

Calculate the Average Directional Index (ADX) for trend strength analysis.

ADX is a non-directional indicator that quantifies trend strength regardless of direction. It ranges from 0 to 100, with higher values indicating stronger trends. The calculation includes +DI and -DI (Directional Indicators) that measure upward and downward price movement strength.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for ADX calculation. Defaults to 14.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A DataFrame with ‘ADX’, ‘+DI’, and ‘-DI’ columns.

Return type:

pandas.DataFrame

Example

Calculate ADX and assess trend strength:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 104, 106, 108, 110, 112, 114, 116])
>>> high = pd.Series([101, 103, 105, 107, 109, 111, 113, 115, 117])
>>> low = pd.Series([99, 101, 103, 105, 107, 109, 111, 113, 115])
>>> adx_data = close.indicators.adx(high, low, window_size=5)
>>> strong_trend = adx_data['ADX'] > 25  # Strong trend identification
>>> bullish = adx_data['+DI'] > adx_data['-DI']  # Uptrend
>>> print(f"ADX: {adx_data['ADX'].iloc[-1]:.1f}")
ADX: 45.2

Note

• ADX > 25: Strong trend (regardless of direction)

• ADX < 20: Weak trend or sideways market

• +DI > -DI: Uptrend strength

• -DI > +DI: Downtrend strength

parabolic_sar(high, low, af_start=0.02, af_increment=0.02, af_maximum=0.2)

Calculate the Parabolic Stop and Reverse (SAR) for trend following.

Parabolic SAR is a trend-following indicator that provides potential reversal points and trailing stop levels. It appears as dots above or below price: dots below indicate uptrends, dots above indicate downtrends. The indicator uses an acceleration factor that increases over time for sensitivity.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• af_start (float, optional) – Initial acceleration factor. Defaults to 0.02.

• af_increment (float, optional) – Increment added to acceleration factor when new extreme is reached. Defaults to 0.02.

• af_maximum (float, optional) – Maximum acceleration factor value. Defaults to 0.2.

Returns:

A Series representing Parabolic SAR values.

Return type:

pandas.Series

Example

Calculate Parabolic SAR for trend identification and stops:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110])
>>> high = pd.Series([101, 103, 105, 104, 106, 108, 107, 109, 111])
>>> low = pd.Series([99, 101, 103, 102, 104, 106, 105, 107, 109])
>>> sar = close.indicators.parabolic_sar(high, low)
>>> uptrend = close > sar    # Price above SAR = uptrend
>>> downtrend = close < sar  # Price below SAR = downtrend
>>> print(f"Latest SAR: {sar.iloc[-1]:.2f}")
Latest SAR: 99.45

Note

• Price above SAR: Uptrend (SAR acts as support)

• Price below SAR: Downtrend (SAR acts as resistance)

• SAR flip: Potential trend reversal signal

• Use SAR as trailing stop-loss levels

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 average value over a defined number of periods.

Parameters:

• window_size (int, optional) – The size of the moving window, representing the number of periods over which to calculate the average. Defaults to 20.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A pandas Series containing the calculated SMA values.

Return type:

pandas.Series

Example

Calculate 20-period Simple Moving Average:

>>> import pandas as pd
>>> import rhoa
>>> prices = pd.Series([100, 102, 101, 103, 105, 104, 106])
>>> sma = prices.indicators.sma(window_size=5)
>>> print(sma.iloc[4])  # First valid SMA value
102.2

Note

The first window_size - 1 values will be NaN since there aren’t enough observations to calculate the average.

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. This method is commonly used in financial time series to smooth data and compute trends. Unlike simple moving averages, EWMA gives more weight to recent observations.

Parameters:

• window_size (int, optional) – 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. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to False.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the calculated EWMA values.

Return type:

pandas.Series

Example

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.indicators.ewma(window_size=5)
>>> print(f"Latest EWMA: {ewma.iloc[-1]:.2f}")
Latest EWMA: 105.45

Note

EWMA responds more quickly to recent price changes compared to SMA, making it useful for trend following strategies.

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. The window size parameter determines the span of the exponentially weighted period. EWMV is useful for measuring volatility that adapts more quickly to recent price changes.

Parameters:

• window_size (int, optional) – The span of the exponential window. Determines the level of smoothing applied to the variance calculation. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to True.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the exponentially weighted moving

variance of the input series.

Return type:

pandas.Series

Example

Calculate exponentially weighted moving variance:

>>> import pandas as pd
>>> import rhoa
>>> prices = pd.Series([100, 102, 99, 103, 105, 101, 106, 104])
>>> ewmv = prices.indicators.ewmv(window_size=5)
>>> print(f"Latest variance: {ewmv.iloc[-1]:.2f}")
Latest variance: 6.24

Note

Higher variance values indicate increased volatility in the price series. The variance is always non-negative.

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.

Parameters:

• window_size (int, optional) – The span or window size for the exponentially weighted moving calculation. Smaller spans apply heavier weighting to more recent data points, while larger spans provide smoother results. Defaults to 20.

• adjust (bool, optional) – Divide by decaying adjustment factor in beginning periods. When True, the weights are normalized by the sum of weights. Defaults to True.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing the exponentially weighted moving

standard deviation values.

Return type:

pandas.Series

Example

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.indicators.ewmstd(window_size=5)
>>> print(f"Latest volatility: {ewmstd.iloc[-1]:.2f}")
Latest volatility: 2.50

Note

The relationship EWMSTD² = EWMV holds. This indicator is commonly used for volatility-based trading strategies and risk management.

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 change of price movements on a scale of 0 to 100. It helps identify overbought (typically >70) and oversold (typically <30) market conditions. RSI is one of the most widely used technical indicators in trading.

Parameters:

• window_size (int, optional) – The size of the rolling window used to calculate the moving averages of gains and losses. Traditional value is 14. Defaults to 14.

• edge_case_value (float, optional) – The RSI value to use when avg_loss == 0 (no losses occurred). Common values: 100.0 (infinite RS, default), 50.0 (neutral), or float(‘nan’). Defaults to 100.0.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A pandas Series containing RSI values between 0 and 100.

Return type:

pandas.Series

Example

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.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

Note

• RSI > 70: Generally considered overbought (potential sell signal)

• RSI < 30: Generally considered oversold (potential buy signal)

• RSI around 50: Neutral momentum

stochastic(self, high, low, k_window=14, d_window=3, min_periods=None, center=False, **kwargs)

Calculate the Stochastic Oscillator (%K and %D) for momentum analysis.

The Stochastic Oscillator compares a closing price to its price range over a given time period. It generates values between 0 and 100, where values above 80 typically indicate overbought conditions and values below 20 indicate oversold conditions.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• k_window (int, optional) – Number of periods for %K calculation. Defaults to 14.

• d_window (int, optional) – Number of periods for %D calculation (SMA of %K). Defaults to 3.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A DataFrame with ‘%K’ and ‘%D’ columns representing

the stochastic values.

Return type:

pandas.DataFrame

Example

Calculate Stochastic Oscillator and identify signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> stoch = close.indicators.stochastic(high, low, k_window=5, d_window=3)
>>> overbought = stoch['%K'] > 80  # Potential sell signals
>>> oversold = stoch['%K'] < 20   # Potential buy signals
>>> print(f"%K: {stoch['%K'].iloc[-1]:.1f}, %D: {stoch['%D'].iloc[-1]:.1f}")
%K: 75.0, %D: 72.3

Note

• %K > 80: Overbought (potential sell signal)

• %K < 20: Oversold (potential buy signal)

• %K crossing above %D: Bullish signal

• %K crossing below %D: Bearish signal

williams_r(self, high, low, window_size=14, min_periods=None, center=False, **kwargs)

Calculate Williams %R for momentum and overbought/oversold analysis.

Williams %R is a momentum indicator that measures overbought and oversold levels. It oscillates between -100 and 0, with readings above -20 indicating overbought conditions and readings below -80 indicating oversold conditions. It’s essentially an inverted Stochastic Oscillator.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for Williams %R calculation. Defaults to 14.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series representing Williams %R values (-100 to 0).

Return type:

pandas.Series

Example

Calculate Williams %R and identify trading signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> wr = close.indicators.williams_r(high, low, window_size=5)
>>> overbought = wr > -20  # Potential sell signals
>>> oversold = wr < -80   # Potential buy signals
>>> print(f"Williams %R: {wr.iloc[-1]:.1f}")
Williams %R: -25.0

Note

• Williams %R > -20: Overbought (potential sell signal)

• Williams %R < -80: Oversold (potential buy signal)

• Values closer to 0: Stronger momentum

• Values closer to -100: Weaker momentum

cci(self, high, low, window_size=20, min_periods=None, center=False, **kwargs)

Calculate the Commodity Channel Index (CCI) for momentum analysis.

CCI is a momentum-based oscillator that measures the variation of a security’s price from its statistical mean. It oscillates above and below zero, with readings above +100 indicating overbought conditions and readings below -100 indicating oversold conditions.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for calculating the CCI. Defaults to 20.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series representing the calculated CCI values.

Return type:

pandas.Series

Example

Calculate CCI and identify trading signals:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106, 108, 107])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107, 109, 108])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105, 107, 106])
>>> cci = close.indicators.cci(high, low, window_size=5)
>>> overbought = cci > 100   # Potential sell signals
>>> oversold = cci < -100    # Potential buy signals
>>> print(f"Latest CCI: {cci.iloc[-1]:.1f}")
Latest CCI: 85.2

Note

• CCI > +100: Overbought condition (potential sell signal)

• CCI < -100: Oversold condition (potential buy signal)

• CCI around 0: Normal trading range

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 moving averages of a security’s price. It consists of three components: the MACD line, signal line, and histogram, which together provide insights into trend direction and momentum changes.

The MACD line is the difference between the short-term and long-term EMAs. The signal line is an EMA of the MACD line. The histogram shows the difference between MACD and signal lines.

Parameters:

• short_window (int, optional) – Length of the short-term EMA window. Defaults to 12.

• long_window (int, optional) – Length of the long-term EMA window. Defaults to 26.

• signal_window (int, optional) – Length of the signal EMA window. Defaults to 9.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A DataFrame with columns ‘macd’, ‘signal’, and ‘histogram’.

Return type:

pandas.DataFrame

Example

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.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

Note

• Bullish signal: MACD line crosses above signal line

• Bearish signal: MACD line crosses below signal line

• Histogram > 0: MACD above signal (bullish momentum)

• Histogram < 0: MACD below signal (bearish momentum)

adx(self, high, low, window_size=14, min_periods=None, **kwargs)

Calculate the Average Directional Index (ADX) for trend strength analysis.

ADX is a non-directional indicator that quantifies trend strength regardless of direction. It ranges from 0 to 100, with higher values indicating stronger trends. The calculation includes +DI and -DI (Directional Indicators) that measure upward and downward price movement strength.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• window_size (int, optional) – Number of periods for ADX calculation. Defaults to 14.

• min_periods (int, optional) – Minimum observations in window required to have a value. Defaults to None.

• **kwargs – Additional keyword arguments passed to pandas ewm function.

Returns:

A DataFrame with ‘ADX’, ‘+DI’, and ‘-DI’ columns.

Return type:

pandas.DataFrame

Example

Calculate ADX and assess trend strength:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 104, 106, 108, 110, 112, 114, 116])
>>> high = pd.Series([101, 103, 105, 107, 109, 111, 113, 115, 117])
>>> low = pd.Series([99, 101, 103, 105, 107, 109, 111, 113, 115])
>>> adx_data = close.indicators.adx(high, low, window_size=5)
>>> strong_trend = adx_data['ADX'] > 25  # Strong trend identification
>>> bullish = adx_data['+DI'] > adx_data['-DI']  # Uptrend
>>> print(f"ADX: {adx_data['ADX'].iloc[-1]:.1f}")
ADX: 45.2

Note

• ADX > 25: Strong trend (regardless of direction)

• ADX < 20: Weak trend or sideways market

• +DI > -DI: Uptrend strength

• -DI > +DI: Downtrend strength

parabolic_sar(self, high, low, af_start=0.02, af_increment=0.02, af_maximum=0.2)

Calculate the Parabolic Stop and Reverse (SAR) for trend following.

Parabolic SAR is a trend-following indicator that provides potential reversal points and trailing stop levels. It appears as dots above or below price: dots below indicate uptrends, dots above indicate downtrends. The indicator uses an acceleration factor that increases over time for sensitivity.

Parameters:

• high (pandas.Series) – A Series containing the high prices.

• low (pandas.Series) – A Series containing the low prices.

• af_start (float, optional) – Initial acceleration factor. Defaults to 0.02.

• af_increment (float, optional) – Increment added to acceleration factor when new extreme is reached. Defaults to 0.02.

• af_maximum (float, optional) – Maximum acceleration factor value. Defaults to 0.2.

Returns:

A Series representing Parabolic SAR values.

Return type:

pandas.Series

Example

Calculate Parabolic SAR for trend identification and stops:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 104, 103, 105, 107, 106, 108, 110])
>>> high = pd.Series([101, 103, 105, 104, 106, 108, 107, 109, 111])
>>> low = pd.Series([99, 101, 103, 102, 104, 106, 105, 107, 109])
>>> sar = close.indicators.parabolic_sar(high, low)
>>> uptrend = close > sar    # Price above SAR = uptrend
>>> downtrend = close < sar  # Price below SAR = downtrend
>>> print(f"Latest SAR: {sar.iloc[-1]:.2f}")
Latest SAR: 99.45

Note

• Price above SAR: Uptrend (SAR acts as support)

• Price below SAR: Downtrend (SAR acts as resistance)

• SAR flip: Potential trend reversal signal

• Use SAR as trailing stop-loss levels

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. The bands expand and contract based on market volatility, providing insights into potential overbought/oversold conditions and price volatility patterns.

Parameters:

• window_size (int, optional) – The size of the rolling window used for computing the moving average and standard deviation. Defaults to 20.

• num_std (float, optional) – The number of standard deviations to add/subtract from the moving average to calculate the upper and lower bands. Defaults to 2.0.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A DataFrame with columns ‘upper_band’, ‘middle_band’,

and ‘lower_band’.

Return type:

pandas.DataFrame

Example

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.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

Note

• Price touching upper band: Potentially overbought

• Price touching lower band: Potentially oversold

• Narrow bands: Low volatility (squeeze)

• Wide bands: High volatility (expansion)

atr(self, high, low, window_size=14, min_periods=None, center=False, **kwargs)

Calculate the Average True Range (ATR) for volatility measurement.

ATR measures market volatility by calculating the average of true ranges over a specified period. True range is the maximum of: (high - low), (high - previous close), or (low - previous close). ATR is widely used for position sizing and stop-loss placement.

Parameters:

• high (pandas.Series) – A Series representing the high prices.

• low (pandas.Series) – A Series representing the low prices.

• window_size (int, optional) – Length of the rolling window for calculating the average true range. Defaults to 14.

• min_periods (int, optional) – Minimum number of observations in window required to have a value. Defaults to None.

• center (bool, optional) – Whether to center the labels in the result. Defaults to False.

• **kwargs – Additional keyword arguments passed to pandas rolling function.

Returns:

A Series containing the calculated ATR values.

Return type:

pandas.Series

Example

Calculate ATR for position sizing:

>>> import pandas as pd
>>> import rhoa
>>> close = pd.Series([100, 102, 101, 103, 105, 104, 106])
>>> high = pd.Series([101, 103, 102, 104, 106, 105, 107])
>>> low = pd.Series([99, 101, 100, 102, 104, 103, 105])
>>> atr = close.indicators.atr(high, low, window_size=5)
>>> # Use ATR for stop-loss: 2 * ATR below entry
>>> stop_distance = 2 * atr.iloc[-1]
>>> print(f"ATR: {atr.iloc[-1]:.2f}, Stop distance: {stop_distance:.2f}")
ATR: 1.80, Stop distance: 3.60

Note

Higher ATR values indicate higher volatility. ATR is commonly used for setting stop-losses and position sizing in trading strategies.