Table 2.
Density Forecast Accuracy as Measured by CRPS
Forecast Horizon
Variable01234Beginning of the Evaluation
RGDP
(SV relative) 3.01%** 7.50%*** 7.96%*** 9.27%*** 7.58%*** 1983:Q4
(FE-SIMPLE) 0.82 1.02 1.10 1.16 1.17
UNRATE
(SV relative) 1.78%* 2.82%** 3.56%** 3.44%* 2.25% 1983:Q4
(FE-SIMPLE) 0.08 0.17 0.25 0.34 0.43
PGDP
(SV relative) 1.03% 1.41% 1.83% 2.59% 3.00% 1983:Q4
(FE-SIMPLE) 0.50 0.56 0.60 0.63 0.68
CPI
(SV relative) 1.98% 2.35% 1.49% 1.63% 2.35% 1996:Q3
(FE-SIMPLE) 0.66 1.05 1.09 1.10 1.10
TBILL
(SV relative) 11.36%*** 13.99%*** 13.00%*** 9.85%** 6.86% 1996:Q3
(FE-SIMPLE) 0.07 0.23 0.40 0.58 0.76
Forecast Horizon
Variable01234Beginning of the Evaluation
RGDP
(SV relative) 3.01%** 7.50%*** 7.96%*** 9.27%*** 7.58%*** 1983:Q4
(FE-SIMPLE) 0.82 1.02 1.10 1.16 1.17
UNRATE
(SV relative) 1.78%* 2.82%** 3.56%** 3.44%* 2.25% 1983:Q4
(FE-SIMPLE) 0.08 0.17 0.25 0.34 0.43
PGDP
(SV relative) 1.03% 1.41% 1.83% 2.59% 3.00% 1983:Q4
(FE-SIMPLE) 0.50 0.56 0.60 0.63 0.68
CPI
(SV relative) 1.98% 2.35% 1.49% 1.63% 2.35% 1996:Q3
(FE-SIMPLE) 0.66 1.05 1.09 1.10 1.10
TBILL
(SV relative) 11.36%*** 13.99%*** 13.00%*** 9.85%** 6.86% 1996:Q3
(FE-SIMPLE) 0.07 0.23 0.40 0.58 0.76

The table reports CRPS results for out-of-sample density forecasts. The sample uses predictions made from the date given in the right-most column through 2017:Q4 (and realized forecast errors as far as available). For each variable, the top row reports the relative CRPS calculated as the percentage decrease of the CRPS when using SV rather than FE-SIMPLE; positive numbers indicate improvement of SV over the FE-SIMPLE case. The bottom row reports the CRPS for the FE-SIMPLE case, which has been estimated over rolling windows with sixty quarterly observations. Statistical significance of the differences in average CRPS, assessed with a Diebold and Mariano (1995) test, is indicated by *, **, or ***, corresponding to 10%, 5%, and 1% significance, respectively.

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