The Necessity of Moving Averages in Dynamic Linear Regression Models

Abstract

Abstract Consensus from the debate over lagged dependent variables in dynamic linear regression models advises that including enough lags of the dependent and independent variables will fully model autocorrelation in the error term. But this approach fails to account for a long‐neglected source of autocorrelation in the error term—moving averages—which cannot be represented with a finite number of lags. Approximating moving averages results in either inconsistent or inefficient estimates of relevant quantities of interest, a claim demonstrated here via Monte Carlo simulations and three empirical demonstrations. Ultimately, we argue that moving averages should be a standard part of dynamic analysis and offer guidance for incorporating them into various modeling strategies.