An Estimating Equation Approach for Robust Confidence Intervals for Autocorrelations of Stationary Time Series
Paper joint with Taeyoon Hwang
Abstract:
This paper develops an estimating equation approach to construct confidence intervals for autocorrelation for time series with general stationary serial correlation structures. Inference is heteroskedasticity and autocorrelation robust (HAR). It is well known that the Bartlett (1946) formula can provide invalid inference when innovations are not independent and identically distributed (i.i.d.). Romano and Thombs (1996) derive the asymptotic distribution of sample autocorrelations under weak assumptions but avoid estimation of the variances of sample autocorrelation and suggest resampling schemes to obtain confidence intervals. As an alternative we provide an easy to implement estimating equation approach for estimating autocorrelation and their variances. The asymptotic variances take sandwich forms which can be estimated using well known HAR variance estimators. Resulting t-statistics can be implemented with fixed-smoothing critical values. Monte Carlo simulations show our approach is robust to innovations that are not i.i.d. and works reasonably well across various serial correlation structures. An empirical illustration using S&P 500 index returns shows that conclusions about market efficiency and volatility clustering during pre and post-Covid periods using our approach contrast with conclusions using traditional (and often incorrectly used) methods.