Forecasting using a large panel of predictors: Bayesian model averaging and principal components regression

We study the out-of-sample forecast performance of two alternative methods for dealing with dimensionality: Bayesian model Averaging (BMA) and principal components regression (PCR). We conduct a different out-of-sample investigation in which the predictors are chosen jointly for both output and inflation using Bayesian variable selection in each out-of-sample recursion using information available at the time of the forecast. This framework implies stochastic nonparametric time-varying reduced form which offers flexibility in capturing structural changes and instabilities of unknown forms. While the competing forecasts are highly correlated, PCR performed marginally better than BMA in terms of mean-squared forecast error. However, this marginal edge in the average global out-of-sample performance hides important changes in the local forecasting power. An analysis of the Theil index indicates that the loss of performance of PCR is due mainly to its exuberant biases in matching the mean of the two series especially the inflation series. BMA forecasts series matches the first and second moments of the GDP and inflation series very well with practically zero biases and very low volatility. The fluctuation statistic that measures the relative local performance shows that BMA performed consistently better than PCR and the naive random walk benchmark over the period prior to 1985. Thereafter, the performance of both BMA and PCR was relatively modest compared to the naive benchmark.