Estimated factors. The previous results suggest that it is of interest to examine the first few estimated factors. The interpretation of the factors is simplest for the case of the balanced panel, for here the factors are the eigenvectors of ordered by the magnitude of the associated eigenvalues. We therefore focus here on the full-sample estimates of the factors using the balanced panel. Only this ordering of the factors is considered. Because the estimates here are for the full sample, these factors in general differ from those used in the recursive out-of-sample forecasting exercise.

Figure 1 displays the R s of the regressions of the 170 individual time series in the balanced panel against each of the six factors, plotted as bar charts with one chart for each factor. (The series are grouped by category and ordered numerically using the ordering in the appendix.) Broadly speaking, the first factor loads primarily on output and employment; the second factor on inflation and interest rate spreads; the third, on unemployment; the fourth, on housing starts and orders; the fifth, on stock returns and money growth; and the sixth, on new orders. In this sense, the first factor may be thought of as an output factor, the second as an inflation factor, the third as an unemployment factor, etc. Taken together, these six factors account for 47% of the variance of the 170 monthly time series in the balanced panel, as measured by the trace-R ; the first twelve factors together account for 61 % of the variance of these series.

The factors are plotted in figure 2, each along with an individual transformed series suggested by the variance decompositions in figure 1. For example, the first factor is plotted with the monthly growth rate of industrial production, both transformed to have unit standard deviation. Interestingly, the factors generally contain considerable high frequency power, for example, factor #3 has low frequency behavior similar to the unemployment rate, but has much more pronounced monthly fluctuations.