TABLE 5 – CONTINUOUS RANKED PROBABILITY SCORE OF DENSITY FORECASTS

||Average for<br>TPN Density Forecasts<br>(BCEF method)|Weighted Average for TPN<br>Density Forecasts<br>(BCEF method)<br>Average for<br>Normal Density Forecasts<br>(Varying HFE Standard<br>|<br> <br>Weighted Average for<br>Normal Density Forecasts<br>(Varying HFE Standard<br>|
|---|---|---|---|
|||<br>Deviation Across Horizons)|<br>Deviation Across Horizons)|
|Panel A. Monthly Averag<br>|e Forecast Scores Across the<br>|Period of 2005–2015 and Three Annual Time-Horizons<br> <br>|h={0,1,2}.<br>|
|January|1.6|0.55<br>1.79|0.62|
|February|1.55|0.58<br>1.79|0.67|
|March|1.51|0.61<br>1.79|0.72|
|April|1.55|0.66<br>1.79|0.77|
|May|1.51|0.69<br>1.79|0.82|
|June|1.45|0.7<br>1.76|0.85|
|July|1.44|0.73<br>1.76|0.89|
|August|1.47|0.79<br>1.76|0.94|
|September|1.46|0.82<br>1.79|1|
|October|1.46|0.86<br>1.76|1.03|
|November|1.47|0.9<br>1.76|1.08|
|December|1.45|0.93<br>1.76|1.12|
|<br>Panel B. Annual Average|<br>Forecast Scores Across Mont|<br> <br>hly Observations Over 2005–2015 and Three Annual Ti|<br>me-Horizonsh={0,1,2}.|
|2005|1.04|0.62<br>1.5|0.9|
|2006|1.26|0.61<br>1.6|0.78|
|2007|2.6|0.92<br>2.65|0.99|
|2008|2.69|1.43<br>2.82|1.46|
|2009|1.6|1.03<br>1.97|1.15|
|2010|1.27|0.63<br>1.55|0.77|
|2011|1.23|0.56<br>1.47|0.68|
|2012|1.07|0.49<br>1.38|0.65|
|2013|0.89|0.4<br>1.32|0.62|
|2014|0.93|0.59<br>1.29|0.83|
|2015|0.72|0.57<br>0.97|0.77|
|Panel C. Horizon Averag|e Forecast Scores Across Mon|thly Observations Over 2005–2015.||
|h= 0|1.15|0.97<br>1.34|1.14|
|h= 1|1.73|0.89<br>2.07|1.07|
|h= 2|1.65|0.30<br>1.95|0.36|
|Panel D. Average Foreca|st Scores Across Monthly Obs|ervations Over 2005–2015 and Three Annual Time-Ho|rizonsh={0,1,2}.|
|Aggregated Score|490.90|243.15<br>583.41|289.45|

Note: The weighted scores use masses derived following the rule presented in Equation (32). The weights penalize the forecasts under the following principle: when a forecast is elicited, it is expected that it has better accuracy if it is produced closer to the realization period than when it is released with a further horizon. In this sense, the closer to the realization period, the more punished (weighted) the elicited forecast. HFE stands for historical forecast error. The monthly estimated density forecasts cover the period of October 2005–August 2015. Forecasts generated in 2014 are evaluated only with the realizations of 2014 and 2015. Predictions made in 2015 are scored using realizations of 2015. Scores of naïve density forecasts generated using the rule of thumb of a fixed HFE standard deviation across the three forecasting horizons (results are available upon request) were estimated and not presented in this table. These latter scoring results remained the same as the ones shown in this table: BCEF density forecasts outperform naïve density predictions.

The CRPS scores overwhelmingly show more accurate density forecasts—lower score values—for the BCEF density forecasts than for the naïve predictions. The unweighted and weighted CRPS results are robust over four views: across horizons, months, years, and in the aggregated form. In this regard, the CRPS scores also indicate that the BCEF fan charts are 27