The distribution of rolling regression estimators

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