Forecasting Using a Large Number of Predictors: Bayesian Model Averaging Versus Principal Components Regression

Abstract

We study the performance of Bayesian model averaging as a forecasting method for a large panel of time series and compare its performance to principal components regression (PCR). We show empirically that these forecasts are highly correlated implying similar mean-square forecast errors. Applied to forecasting Industrial production and inflation in the United States, we find that the set of variables deemed informative changes over time which suggest temporal instability due to collinearity and to the of Bayesian variable selection method to minor perturbations of the data. In terms of mean-squared forecast error, principal components based forecasts have a slight marginal advantage over BMA. However, this marginal edge of PCR in the average global out-of-sample performance hides important changes in the local forecasting power of the two approaches. 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 benchmark (random walk) over the period prior to 1985. Thereafter, the performance of both BMA and PCR was relatively modest compared to the naive benchmark.