All series on this list were subjected to two preliminary steps: possible transformation by taking logarithms, and possible first differencing. The decision to take logarithms or to first difference the series was judgmentally made. In general, logarithms were taken for all nonnegative series that were not already in rates or percentage units. In general, first differences were taken of real and nominal quantity series and of price indexes. A code summarizing these transformations is given for each series in Appendix B. After these transformations, all series were further standardized to have sample mean zero and unit sample variance.
The factors were estimated using only contemporaneous values of Xt (no stacking of lagged values of Xt). The factors were computed using the algorithms described in section 2. A total of к = 12 factors were estimated.

In general the error term et in (2.2) can be serially correlated. This suggests considering a variant of (2.2) in which lagged values of the dependent variable also appear as predictors. We therefore consider diffusion index forecasts of the form,
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where {£-J are the estimated factors. Given q and p, the coefficients of (5.1) were estimated by OLS. Four variants of (5.1) are reported, each with different treatment of q: (i) the number of factors recursively selected by BIC, 1 <q< 12, and no autoregressive components (p=0); (ii) the number of factors recursively selected by BIC, 1 <q< 12, and autoregressive components recursively estimated by BIC (0<p< 5); (iii) a fixed number of factors and p=0; and (iv) a fixed number of factors and p selected by BIC (0<p<5).
Autoregressive forecast. The autoregressive forecast is a univariate forecast based on the model,
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where p is selected recursively by BIC (0<p<5).