Quant Statistics

• You need to verify whether a price or factor series is stationary before running regressions or building models, avoiding spurious results.
• You are researching pairs trading or statistical arbitrage and need to test for cointegration and compute hedge ratios and mean-reversion half-lives.
• You are validating a strategy's Sharpe ratio or alpha with bootstrap confidence intervals to determine whether performance is statistically significant rather than due to chance.
• You are diagnosing an OLS regression for heteroskedasticity, autocorrelation, or multicollinearity before interpreting factor exposures or risk-model outputs.

• You need purely descriptive or exploratory data summaries (means, correlations, histograms) without any inferential or time-series testing — simpler tools are sufficient.
• Your workflow is real-time, high-frequency signal generation where GARCH or bootstrap computations are too slow for the required latency.
• You are working with very short data histories (fewer than a few dozen observations), where the asymptotic assumptions behind ADF, GARCH, and Ljung-Box tests may not hold reliably.

Runs the Augmented Dickey-Fuller test on any time series and returns the test statistic, p-value, lags used, and 1%/5%/10% critical values. Clear decision rules map p-value ranges to actionable conclusions — use directly, difference the series, or apply cointegration methods.

Tests whether two non-stationary series share a long-run equilibrium, computes the OLS hedge ratio, constructs the spread, and estimates the mean-reversion half-life. Z-score thresholds for entry and exit signals are built into the output, providing the statistical foundation for pairs trading.

Fits a GARCH(1,1) model via the arch library and returns ω, α, β, persistence, long-run volatility, current conditional volatility, and a 5-day-ahead volatility forecast with AIC/BIC. Guidance on EGARCH and GJR-GARCH variants covers asymmetric leverage effects common in equity and crypto markets.

Runs White and Breusch-Pagan heteroskedasticity tests, Durbin-Watson and Ljung-Box autocorrelation tests, and VIF multicollinearity checks in a single workflow. Each test returns an interpretation and a concrete fix recommendation (e.g., HAC/Newey-West standard errors or WLS).

Estimates confidence intervals for any statistic — Sharpe ratio, alpha, maximum drawdown distribution — via resampling without distributional assumptions. A dedicated bootstrap_sharpe function flags whether the 95% CI excludes zero, giving a robust significance check for strategy performance.

Provides a quick-reference table of tests matched to common quant questions, and applies Benjamini-Hochberg FDR correction via statsmodels.stats.multitest when evaluating many factors or strategies simultaneously. Built-in rules of thumb link Sharpe magnitude and backtest length to statistical significance thresholds.

Test two equity or ETF price series for cointegration, estimate the hedge ratio and spread half-life, and generate z-score entry/exit signals. Ongoing cointegration monitoring is supported to detect relationship breakdowns.

Apply stationarity tests to raw factor series, diagnose factor-return regressions for heteroskedasticity and autocorrelation, and use bootstrap Sharpe confidence intervals with FDR correction to distinguish genuine factor premia from statistical noise across a large factor universe.

Fit GARCH(1,1) or asymmetric variants to return series to obtain conditional volatility estimates and short-horizon forecasts. Output parameters and long-run volatility levels feed directly into position sizing or option pricing workflows.

Run the full regression diagnostics checklist — linearity, normality, heteroskedasticity, autocorrelation, multicollinearity, and outliers — before interpreting any OLS-based factor model, ensuring standard errors and t-statistics are reliable.