QuanTAlib/lib/statistics/_index.md

Statistics

"All models are wrong, but some are useful." — George Box

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 Status

Indicator	Full Name	Status	Description
BETA	Beta Coefficient	✅	Asset volatility relative to market. β=1 means market-matched risk.
BIAS	Bias	📋	Percentage deviation from moving average. Measures overextension.
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.
CORRELATION	Correlation (Pearson's)	📋	Linear relationship between two variables. Range: -1 to +1.
COVARIANCE	Covariance	✅	Joint variability of two random variables. Building block for β.
CUMMEAN	Cumulative Mean	📋	Cumulative mean from series start. Ignores NaN values.
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.
MEDIAN	Median	✅	Middle value in sorted window. Robust to outliers.
MODE	Mode	📋	Most frequent value. Use for categorical or discrete data.
PERCENTILE	Percentile	📋	Value below which given percentage of observations fall.
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.
SUM	Rolling Sum	✅	Kahan-Babuška summation. Numerically stable.
THEIL	Theil Index	📋	Inequality measure. Decomposable into within/between group.
VARIANCE	Variance	✅	Average squared deviation from mean. Units are squared.
ZSCORE	Z-Score	📋	Standard deviations from mean. Normalizes different scales.
ZTEST	Z-Test	📋	Hypothesis test comparing sample mean to population mean.

Status Key: ✅ Implemented | 📋 Planned

Selection Guide

Use Case	Recommended	Why
Dispersion measurement	STDDEV, VARIANCE	Standard measures. STDDEV in original units.
Outlier-robust dispersion	MEDIAN, IQR	Median ignores extremes. IQR measures middle 50%.
Central tendency	CMA, MEDIAN	CMA for normal data. MEDIAN for skewed data.
Trend fitting	LINREG	Least squares regression. Provides slope and R².
Distribution shape	SKEW, KURTOSIS	Skew for asymmetry. Kurtosis for tail risk.
Pair relationships	CORRELATION, COVARIANCE, BETA	Correlation normalized. Covariance raw. Beta relative to benchmark.
Regime detection	HURST, ENTROPY	Hurst for trending vs mean-reverting. Entropy for randomness.
Normality testing	JB	Quick normality check before parametric tests.

Statistical Concepts

Concept	Implemented As	Interpretation
Location	CMA, MEDIAN	Where is the center?
Spread	VARIANCE, STDDEV, IQR	How dispersed is data?
Shape	SKEW, KURTOSIS	Is distribution symmetric? Fat-tailed?
Relationship	CORRELATION, COVARIANCE, BETA	How do two series move together?
Trend	LINREG	What is underlying direction?
Memory	HURST	Does past predict future?