Forecast evaluation with factor-augmented models

This paper provides an extension of Diebold-Mariano-West (DMW) forecast accuracy tests to allow for factor-augmented models to be compared with non-nested benchmarks. The out-of- sample approach to forecast evaluation requires that both the factors and the forecasting model parameters are estimated in a rolling fashion, which poses several new challenges which we address in this paper. Firstly, we show the convergence rates of factors estimated in different rolling windows, and then give conditions under which the asymptotic distribution of the DMW test statistic is not affected by factor estimation error. Secondly, we draw attention to the issue of "sign-changing" across rolling windows of factor estimates and factor-augmented model coefficients, caused by the lack of sign identification when using Principal Components Analysis to estimate the factors. We show that arbitrary sign-changing does not affect the distribution of the DMW test statistic, but it does prohibit the construction of valid bootstrap critical values using existing procedures. We solve this problem by proposing a novel new normalization for rolling factor estimates, which has the effect of matching the sign of factors estimated in different rolling windows. We establish the first-order validity of a simple-to-implement block bootstrap procedure and illustrate its properties using Monte Carlo simulations and an empirical application to forecasting U.S. CPI inflation.