Prewhitening and Bandwidth Choice for HAC Estimators

Backtest returns are usually autocorrelated, today's residual leaks into tomorrow's. Ordinary standard errors assume no such leakage, so they understate the true uncertainty and make a mediocre strategy look statistically solid. A Newey-West (HAC) standard error corrects this by weighting nearby-in-time covariances, but the correction needs a bandwidth: how many lags of autocorrelation to include. Pick too few and you're back to understating error; pick too many and the estimate gets noisy and can even lose the positive-definiteness that makes it usable.

Prewhitening runs the return series through a low-order autoregression, keeps the residuals (now much closer to independent), applies the HAC estimator to those, then "recolors" the variance estimate back to account for the AR filter. The intuition: instead of asking a wide, sloppy averaging window to soak up correlation, remove the correlation directly and let the window do a smaller job.

Suppose a signal's raw returns have first-lag autocorrelation of 0.4. Fitting an AR(1) and prewhitening drops the residual autocorrelation toward zero, so a HAC estimator with bandwidth 2 on the residuals can do what a bandwidth of 6–8 would have needed on the raw series. Fewer lags means less estimation noise in the covariance matrix, which in turn means a tighter, more trustworthy confidence interval around the strategy's Sharpe ratio.

The tradeoff is that the AR fit itself is estimated with error, and a badly misspecified prewhitening model can introduce its own bias. In practice, quants treat bandwidth choice (often via the Newey-West or Andrews rule-of-thumb formulas) and prewhitening as complements, not substitutes, prewhiten first, then let an automatic bandwidth rule pick a small number of remaining lags.