Time Varying Three Pass Regression Filter

We propose non parametric estimators for the three pass regression filter for factor extraction from large dimensional datasets when the factor loadings, the proxy and the target equation parameters are allowed to vary stochastically over time. We provide theoretically optimal and empirically efficient solutions for the choice of bandwidth of the kernel-based estimators. Moreover, we prove consistency of the associated fore-casts when both the time and the cross section dimensions of our dataset become large. We also link our proposals with the time varying parameter constrained least squares estimator and with the time varying partial least squares method, and show that these are special cases of our approach. We asses the finite sample performance of our approach by an extensive set of Monte Carlo experiments, also comparing it with other alternatives proposed in the literature. Finally, we illustrate the empirical advantages of our approach in an out of sample forecasting exercise, using a large panel of macroeconomic series to predict key variables of interest.