Statistics

Measures of a window: central tendency, dispersion, quantiles, moments, z-scores, running totals, and cross-series relationships.

Statistics

Windowed summary statistics: central tendency, dispersion, quantiles, moments, and extremes.

Function	Description
Amihud Illiquidity	Rolling mean of |return| / notional (Amihud 2002 illiquidity ratio).
Exponentially-weighted kurtosis	EW excess kurtosis.
Exponentially-weighted mean	Exponentially-weighted moving average (pandas adjust=True).
Exponentially-weighted RMS	EW root-mean-square.
Exponentially-weighted skewness	EW skewness.
Exponentially-weighted standard deviation	EW standard deviation.
Exponentially-weighted variance	EW variance (pandas adjust=True bias-corrected).
Expanding kurtosis	Running bias-corrected excess kurtosis (Fisher) over the whole history.
Expanding mean	Running mean over the whole history since the last reset.
Expanding skewness	Running bias-corrected sample skewness (G1) over the whole history.
Expanding standard deviation	Running sample standard deviation (ddof=1) over the whole history.
Expanding variance	Running sample variance (ddof=1) over the whole history.
Rolling argmax	Window-offset of the trailing-window maximum (TA-Lib MAXINDEX).
Rolling argmin	Window-offset of the trailing-window minimum (TA-Lib MININDEX).
Rolling interquartile range	Q3 minus Q1 over the trailing window.
Rolling kurtosis	Trailing-window excess kurtosis.
Rolling mean absolute deviation	Trailing-window mean absolute deviation from the rolling mean.
Rolling maximum	Trailing-window maximum (monotonic deque).
Rolling mean	Trailing-window arithmetic mean (simple moving average).
Rolling median	Trailing-window median.
Rolling median absolute deviation	Rolling median absolute deviation, median(|x - median|), a robust scale estimate.
Rolling minimum	Trailing-window minimum (monotonic deque).
Rolling min and max	Trailing-window (min, max) returned as a 2-tuple per step.
Rolling percentile	Percentile (rank/window) of the current value in the trailing window.
Rolling quantile	Trailing-window quantile (e.g. 0.25 = lower quartile).
Rolling range	Trailing-window max minus min.
Rolling rank	Rank of the current value within the trailing window (1-based, average tie rule).
Rolling root-mean-square	Trailing-window root-mean-square.
Rolling skewness	Trailing-window skewness.
Rolling standard deviation	Trailing-window sample standard deviation (ddof=1).
Rolling sum	Trailing-window sum.
Rolling variance	Trailing-window sample variance (ddof=1).

Volatility

The size of fluctuations and risk: standard deviation and variance, RMS, range-based OHLC estimators, and ATR.

Function	Description
Average True Range (ATR)	Wilder-smoothed average of TrueRange.
Bollinger Bands	Mean +/- num_std rolling standard deviations.
EW Garman-Klass variance	Var form of the Garman-Klass range-based volatility estimator (OHLC).
EW Garman-Klass volatility	Vol form of the Garman-Klass range-based volatility estimator (OHLC).
Exponentially-weighted Parkinson variance	Var form of the Parkinson range-based volatility estimator (uses high & low).
Exponentially-weighted Parkinson volatility	Vol form of the Parkinson range-based volatility estimator (uses high & low).
Exponentially-weighted RMS	EW root-mean-square.
EW Rogers-Satchell variance	Var form of the Rogers-Satchell drift-robust range-based estimator.
EW Rogers-Satchell volatility	Vol form of the Rogers-Satchell drift-robust range-based estimator.
Exponentially-weighted standard deviation	EW standard deviation.
Exponentially-weighted variance	EW variance (pandas adjust=True bias-corrected).
Expanding standard deviation	Running sample standard deviation (ddof=1) over the whole history.
Expanding variance	Running sample variance (ddof=1) over the whole history.
Keltner Channels	Volatility-adapted envelope: EMA midline plus/minus a multiple of ATR.
Normalised ATR (NATR)	ATR scaled to a percentage of the current close.
Rolling Downside Deviation	Trailing-window downside semideviation: the RMS of returns falling below a minimum acceptable return.
Rolling Garman-Klass variance	Var form of the Garman-Klass range-based volatility estimator (OHLC).
Rolling Garman-Klass volatility	Vol form of the Garman-Klass range-based volatility estimator (OHLC).
Rolling Parkinson variance	Var form of the Parkinson range-based volatility estimator (uses high & low).
Rolling Parkinson volatility	Vol form of the Parkinson range-based volatility estimator (uses high & low).
Rolling range	Trailing-window max minus min.
Rolling root-mean-square	Trailing-window root-mean-square.
Rolling Rogers-Satchell variance	Var form of the Rogers-Satchell drift-robust range-based estimator.
Rolling Rogers-Satchell volatility	Vol form of the Rogers-Satchell drift-robust range-based estimator.
Rolling standard deviation	Trailing-window sample standard deviation (ddof=1).
Rolling variance	Trailing-window sample variance (ddof=1).
Rolling Yang-Zhang variance	Var form of the Yang-Zhang estimator (drift + gap robust).
Rolling Yang-Zhang volatility	Vol form of the Yang-Zhang estimator (drift + gap robust).
True Range (Wilder)	Per-bar true range accounting for overnight gaps (Wilder, 1978).

Standardization & normalization

Put values on a comparable scale: z-scores, affine rescaling, and detrending.

Function	Description
Detrend	x[t] minus its rolling mean.
Exponentially-weighted z-score	Latest sample standardised by EW mean and std.
Linear (affine)	Affine transform: scale * x + shift.
Rolling z-score	Latest sample standardised by trailing-window mean and std.

Cumulative

Running aggregates from the start of the series.

Function	Description
Accumulation/Distribution Line (Chaikin)	Chaikin Accumulation/Distribution Line.
Cumulative maximum	Running maximum from t=0.
Cumulative minimum	Running minimum from t=0.
Cumulative product	Running product from t=0.
Cumulative sum	Running sum from t=0.
Drawdown	Running drawdown from the cumulative peak.
Expanding maximum	Running maximum from t=0.
Expanding minimum	Running minimum from t=0.
Expanding product	Running product from t=0.
Expanding sum	Running sum from t=0.
First finite value	Latch the first finite value seen since reset.
Last finite value	Return the most recent finite value seen since reset.
Maximum drawdown	Worst drawdown experienced so far (since reset).
On-Balance Volume (OBV)	On-Balance Volume: signed cumulative volume by close-direction (Granville, 1963).

Correlation & regression

Relationships between series: correlation, covariance, regression, hedging, pairs, and mean-reversion.

Function	Description
Online Bayesian univariate regression (2->4 posterior fit)	Causal one-step-ahead predictive mean and std plus current slope and intercept via Normal-Inverse-Gamma posterior.
Exponentially-weighted beta	EW CAPM beta: cov(target, regressor) / var(regressor).
Exponentially-weighted correlation	EW Pearson correlation of two parallel streams.
Exponentially-weighted covariance	EW covariance of two parallel streams.
Kyle's Lambda (exponentially weighted)	Exponentially-weighted price-impact slope of return on signed order flow.
Rolling alpha (regression intercept)	Rolling OLS intercept of target on regressor (companion to RollingBeta).
Rolling beta	cov(x, y) / var(y) - regression slope of x on y.
Rolling correlation	Rolling Pearson correlation of two parallel streams.
Rolling covariance	Rolling sample covariance of two parallel streams.
Rolling Hurst Exponent	Rolling-window Hurst exponent via Anis-Lloyd corrected rescaled-range analysis.
Kyle's Lambda (rolling)	Rolling-window price-impact slope of return on signed order flow (Kyle 1985).
Rolling linear regression (2->4 OLS fit)	Full OLS fit returning (slope, intercept, r_squared, stderr).
Rolling Ornstein-Uhlenbeck fit	Rolling MLE fit of a mean-reverting Ornstein-Uhlenbeck process.
Rolling 1st-order polynomial fit	OLS fit y = a + b*t over a trailing window. derivative_order selects value/slope/zero.
Rolling residual std	Standard deviation of the rolling-hedge-adjusted residual y - beta*x.
Rolling spread	x - beta(x,y) * y - hedge-adjusted residual.
Rolling Time-Series Forecast (TSF)	Linear regression of y on time, projected one step ahead. TA-Lib's TSF.