Forecasting results. The results of the simulated out of sample forecasting experiments are reported in table 2 for IP and in table 3 for CPI inflation. The entries are the mean squared error (MSE) of the candidate forecasting model, computed relative to the MSE of the autoregressive forecast (so the autoregressive forecast, which is unreported, has a relative MSE of 1.00). Smaller relative MSEs signify more accurate forecasts.

First consider the results for IP. In the table, “DI” denotes the static diffusion index forecasts (p=0 in (5.1)), and “DIAR” denotes the diffusion index forecasts augmented with lagged monthly IP growth (p selected by recursive BIC in (5.1)). The diffusion index forecasts with BIC factor selection represent substantial improvements over the leading indicator multivariate forecasts. The performance of the diffusion index forecasts is similar whether or not lags of industrial production growth are included as predictors. This is rather surprising, because it implies that essentially all the predictable dynamics of industrial production growth are accounted for by the estimated factors.

The results for the diffusion index models indicate that, among forecasts with fixed numbers of factors, almost all the improvement is obtained after merely two factors are added; indeed, the MSE actually increases upon the addition of the fourth factor (this is possible because the MSE is for pseudo out of sample forecasts). It is also noteworthy that the BIC-selected forecasts outperform any of the fixed-к forecasts. This suggests that the number of factors useful for forecasting IP evolves over time, and that this time variation is picked up by the recursive BIC procedure. The results for the unbalanced and balanced panels are generally similar. The BIC-selected DI RMSEs are the same for the two panels. However, the fixed-к forecasts are generally better for the larger unbalanced panel.