Fractionally Integrated Data and the Autodistributed Lag Model: Results from a Simulation Study

Abstract

Two contributions in this issue, Grant and Lebo and Keele, Linn, and Webb, recommend using an ARFIMA model to diagnose the presence of and estimate the degree of fractional integration, then either (i) fractionally differencing the data before analysis or, (ii) for cointegrated variables, estimating a fractional error correction model. But Keele, Linn, and Webb also present evidence that ARFIMA models yield misleading indicators of the presence and degree of fractional integration in a series with fewer than 1000 observations. In a simulation study, I find evidence that the simple autodistributed lag model (ADL) or equivalent error correction model (ECM) can, without first testing or correcting for fractional integration, provide a useful estimate of the immediate and long-run effects of weakly exogenous variables in fractionally integrated (but stationary) data.