The distribution of rolling regression estimators

Abstract

We establish the asymptotic distribution for rolling linear regression models using various window widths. The limiting distribution depends on the width of the rolling window and on a “bias process” that is typically ignored in practice. Based on the asymptotic distribution, we tabulate critical values used to find uniform confidence intervals for the average values of regression parameters over the windows. We propose a corrected rolling regression technique that removes the bias process by rolling over smoothed parameter estimates. The procedure is illustrated using a series of Monte Carlo experiments. The paper includes an empirical example to show how the confidence bands suggest alternative conclusions about the persistence of inflation.