Data and Leading Indicators
All variables are measured monthly from January 1976 until the month prior to the one-step ahead forecast. The interest rate series are available for the month of the one-step-ahead forecast. All variables except the interest rates are seasonally adjusted.
The number of unemployed workers and the labor force for Wisconsin are estimated and released monthly by the Bureau of Labor Statistics. The unemployment rate is the ratio of these two variables.
The forecasts make use of lagged values of the Wisconsin unemployment rate, plus the following six leading indicators:
· U.S. unemployment rate (civilian population, 16+ years) (Current Population Survey)
· Chicago Fed National Activity Index (CFNAI)
· Interest rate spread (difference between yields on 10-year and 3-month Treasuries)
· High yield spread (difference between yields on AAA and BAA/BBB corporate bonds
· Midwest Housing Starts (new privately owned housing units started) (Census Bureau)
· Midwest Building Permits (new privately owned housing units authorized by building permits) (Census Bureau)
For the sample period, and for each forecast horizon h, 128 separate linear regressions were estimated for the h-step change in the unemployment rate, and point forecasts generated. The regressions differed in regressors included. All variables were included as pairs (two lags).
The forecasts from the 128 models were combined using weights selected by minimizing the leave-h-out cross-validation criterion. (This combines the suggestion of Hansen (Journal of Econometrics, 2008) for one-step-ahead forecasting and that of Hansen and Racine (working paper, 2009) for robust combination.) 16 models received positive weight.
The conditional variances of the h-step changes were estimated by the same regression method as for the point forecasts. The squared error from the combination forecast was regressed on the same set of 128 regressors, and the estimates combined by minimizing the leave-h-out cross-validation criterion.
The 10%, 25%, 75% and 90% quantiles of the scaled forecast errors (scaled by the estimated conditional standard deviations) were estimated using a smooth quantile estimator. The interval forecasts were then constructed as the mean forecast plus the forecast standard deviation (square root of the forecast variance) multiplied by the quantile estimate.