What Is Heteroskedasticity and Autocorrelation Consistent (HAC)?
Heteroskedasticity and Autocorrelation Consistent (HAC) refers to a family of statistical estimators that produce covariance or standard-error estimates that remain consistent when observations have non-constant variance and serial correlation.
Heteroskedasticity means the variance of a return or model error changes over time. Autocorrelation means neighbouring observations are statistically related. Both are common in financial time series, especially in volatility clusters, rolling technical indicator signals, overlapping returns, and algorithmic trading strategy PnL.
HAC estimators are used because many familiar statistics assume independent observations with constant variance. If those assumptions are false, the point estimate can look precise even when the uncertainty estimate is too optimistic. HAC adjusts the estimated variance for both effects, making inference more robust.
The best-known HAC estimator in finance and econometrics is the Newey-West estimator. It estimates a long-run variance by combining the usual variance with lagged autocovariances, usually with weights that decline as the lag increases. This idea is often used when calculating HAC Sharpe, regression t-statistics, model standard errors, and other time-series diagnostics.
HAC is not a cure for overfitting, look-ahead bias, bad data, or a poorly designed backtest. It only improves the uncertainty estimate once the return series or model residuals are otherwise valid.
Literature and references:
Whitney K. Newey and Kenneth D. West, A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, 1987.
Whitney K. Newey and Kenneth D. West, Automatic Lag Selection in Covariance Matrix Estimation, Review of Economic Studies, 1994.
Halbert White, A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity, Econometrica, 1980.
See also