quantitative-statistics

To test for cointegration and stationarity in time series data, you apply the ADF stationarity test and Engle–Granger cointegration test. These procedures validate spread mean-reversion assumptions for pair trading and statistical arbitrage strategies.

Use GARCH volatility modeling on financial returns when you need to capture volatility clustering and persistence. Fitting variants like EGARCH, GJR-GARCH, or FIGARCH provides forecasts that help validate risk and signal inference assumptions.

Run regression diagnostics on backtested trading signals by testing residuals for heteroskedasticity and autocorrelation. This validates factor and strategy hypothesis testing by ensuring inference assumptions hold for financial returns data.

The best way to establish Granger causality for predictive relationships is applying the Granger causality test to your time series. This checks whether lagged returns improve prediction, validating signal inference for quantitative investing workflows.

Yes, you can apply bootstrap confidence intervals to estimate inference for strategy metrics and correct for multiple testing using FDR. This makes backtest conclusions more defensible by addressing false discoveries in factor hypothesis testing.

Quantitative statistics requires deterministic statistical procedures using established econometrics libraries, but has no hard dependencies. It processes price and return series to output structured decisions, diagnostics, and confidence intervals for trading signals.