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Table 4.
Density Forecast Accuracy as Measured by CRPS, VAR-SV Specification
Forecast Horizon
Variable01234Beginning of the Evaluation
RGDP       
(VAR-SV relative) 1.77% 6.77%*** 7.36%*** 7.07%*** 4.80%** 1983:Q4 
(FE-SIMPLE) 0.82 1.02 1.10 1.16 1.17  
UNRATE       
(VAR-SV relative) 12.15%*** 11.34%*** 10.36%*** 9.02%** 6.22% 1983:Q4 
(FE-SIMPLE) 0.08 0.17 0.25 0.34 0.43  
PGDP       
(VAR-SV relative) −2.29% −2.86% −3.00% −3.45% −5.92% 1983:Q4 
(FE-SIMPLE) 0.50 0.56 0.60 0.63 0.68  
CPI       
(VAR-SV relative) 9.86%** −0.41% −1.79% −2.84% −3.53% 1996:Q3 
(FE-SIMPLE) 0.66 1.05 1.09 1.10 1.10  
TBILL       
(VAR-SV relative) 29.74%*** 25.45%*** 25.40%*** 23.76%*** 21.21%*** 1996:Q3 
(FE-SIMPLE) 0.07 0.23 0.40 0.58 0.76  
Forecast Horizon
Variable01234Beginning of the Evaluation
RGDP       
(VAR-SV relative) 1.77% 6.77%*** 7.36%*** 7.07%*** 4.80%** 1983:Q4 
(FE-SIMPLE) 0.82 1.02 1.10 1.16 1.17  
UNRATE       
(VAR-SV relative) 12.15%*** 11.34%*** 10.36%*** 9.02%** 6.22% 1983:Q4 
(FE-SIMPLE) 0.08 0.17 0.25 0.34 0.43  
PGDP       
(VAR-SV relative) −2.29% −2.86% −3.00% −3.45% −5.92% 1983:Q4 
(FE-SIMPLE) 0.50 0.56 0.60 0.63 0.68  
CPI       
(VAR-SV relative) 9.86%** −0.41% −1.79% −2.84% −3.53% 1996:Q3 
(FE-SIMPLE) 0.66 1.05 1.09 1.10 1.10  
TBILL       
(VAR-SV relative) 29.74%*** 25.45%*** 25.40%*** 23.76%*** 21.21%*** 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 VAR-SV rather than FE-SIMPLE; positive numbers indicate improvement of VAR-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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