QuanTAlib/lib/statistics/_index.md

Statistics

Statistical tools applied to price and returns. These indicators quantify relationships, measure dispersion, test hypotheses. Unlike momentum or trend indicators, statistics describe the data itself.

Indicator	Full Name	Description
ACF	Autocorrelation Function	Correlation of time series with lagged copy. For ARMA model identification.
ADF	Augmented Dickey-Fuller Test	Unit root test for stationarity. MacKinnon p-value output [0,1].
BETA	Beta Coefficient	Asset volatility relative to market. β=1 means market-matched risk.
CMA	Cumulative Moving Average	Running average of all values. Welford's algorithm. No window.
COINTEGRATION	Cointegration	Tests if series share long-term equilibrium. Pairs trading foundation.
CONVEXITY	Beta Convexity	Up/Down beta asymmetry. Convexity = (β⁺ - β⁻)². Measures payoff curvature.
CORREL	Correlation	Linear relationship between two variables. Range: -1 to +1.
COVARIANCE	Covariance	Joint variability of two random variables. Building block for β.
ENTROPY	Shannon Entropy	Measures uncertainty/randomness. Higher entropy = less predictable.
GEOMEAN	Geometric Mean	nth root of product. Use for growth rates and ratios.
GRANGER	Granger Causality	Tests if one series helps predict another. Not true causality.
HARMEAN	Harmonic Mean	Reciprocal of arithmetic mean of reciprocals. For rates/ratios.
HURST	Hurst Exponent	Long-term memory. H>0.5: trending. H<0.5: mean-reverting.
IQR	Interquartile Range	P75 - P25. Robust dispersion measure.
JB	Jarque-Bera Test	Normality test using skewness and kurtosis.
KENDALL	Kendall Rank Correlation	Ordinal association. Robust to outliers.
KURTOSIS	Kurtosis	Tail heaviness. High kurtosis = fat tails = more extreme events.
LINREG	Linear Regression	Least squares fit. Outputs slope, intercept, R².
MEANDEV	Mean Absolute Deviation	Outlier-robust dispersion. Core of CCI. MD ≈ 0.7979σ for normal data.
MEDIAN	Median	Middle value in sorted window. Robust to outliers.
MODE	Mode	Most frequent value. Use for categorical or discrete data.
PACF	Partial Autocorrelation Function	Direct correlation at lag k after removing intermediate effects. For AR model identification.
PERCENTILE	Percentile	Value below which given percentage of observations fall.
POLYFIT	Polynomial Fitting	Least-squares polynomial regression.
QUANTILE	Quantile	Divides distribution into equal probability intervals.
SKEW	Skewness	Distribution asymmetry. Positive: right tail. Negative: left tail.
SPEARMAN	Spearman Rank Correlation	Pearson on ranks. Measures monotonic relationship.
STDDEV	Standard Deviation	Square root of variance. Same units as data.
STDERR	Standard Error of Regression	OLS residual scatter over rolling window. Quantifies trend fit quality.
SUM	Rolling Sum	Kahan-Babuška summation. Numerically stable.
THEIL	Theil Index	Inequality measure. Decomposable into within/between group.
TRIM	Trimmed Mean MA	Mean after discarding extreme percentiles.
VARIANCE	Variance	Average squared deviation from mean. Units are squared.
WAVG	Weighted Average	Generic weighted mean.
WINS	Winsorized Mean MA	Mean with extreme values clamped to percentile bounds.
ZSCORE	Z-Score	Standard deviations from mean. Normalizes different scales.
ZTEST	Z-Test	One-sample t-test statistic against hypothesized mean.