Time-varying forecast combination for factor-augmented regressions with smooth structural changes

This study proposes a time-varying forecast combination for factor-augmented (TVFCFA) regressions with smooth structural changes. First, we establish the limiting distribution of the estimators of the time-varying factor-augmented regressions. To estimate the optimal time-varying combination weights, we propose a local leave-l-out cross-validation (LLOCV) criterion that is asymptotically unbiased for the local mean squared forecast error (LMSFE). The TVFCFA method was shown to be asymptotically optimal in the sense that its LMSFE attains the infeasible lower bound. We establish the convergence rate of the selected weights and demonstrate that the TVFCFA method automatically assigns all weights to correctly specified models. Because the overfitted models have nonzero weights, the TVFCFA estimator asymptotically follows a nonstandard distribution. To obtain an asymptotic normal distribution, we propose a penalized LLOCV criterion such that the weights for the overfitted models asymptotically converge to zero. The TVFCFA estimator, with weights that minimize the penalized LLOCV, asymptotically follows a normal distribution, and the convergence rate of the weights assigned to the overfitted models is inversely proportional to the penalized factor. A Monte Carlo simulation shows that the TVFCFA method outperforms competing model averaging and selection methods that are popular in the literature. Moreover, an empirical application of the TVFCFA method to inflation forecasts demonstrates its superiority.