Ll model involves as many as 14 regressors) and large BMF models. The former are slightly better when the sample ends in 2008; the latter over the full sample, suggesting that more information became relevant during the crisis. We have also experimented (in Carriero et al. (2013)) with different subgroups of the indicators. Perhaps the most interesting finding is that financial indicators, by themselves, do poorly in forecasting current quarter GDP growth. However, in line with the comparison of results across samples that was mentioned above, including financial indicators with other indicators helps the RRx-001 cost models (a little) during the recent crisis. Finally, rolling estimation of the BMF models with constant volatilities generates systematically higher RMSEs than recursive estimation of the same models. This finding suggests that the efficiency losses from using a smaller set of observations are larger than the gains from achieving partial robustness to possible breaks. The main message that we can take from the point forecast evaluation is that overall our BMF method is superior to AR model forecasts and comparable with survey forecasts, though the surveys performed a little better during the crisis. However, a major advantage of our approach is that it also easily delivers density and interval forecasts, and, as we shall now see, in this context the stochastic volatility specification that we adopt becomes quite relevant.Realtime Nowcasting5.3. Density forecasts: average predictive scores To assess the calibration of density forecasts, Table 3 provides average log-score comparisons of our BMF and BMFSV nowcasting models, taking an ARSV model as the benchmark (since previous research has shown that stochastic volatility improves density accuracy of AR forecasts). To facilitate comparisons, the first row of each part of Table 3 provides the average log-score of the ARSV forecast; the remaining rows provide the score of each other model forecast less the benchmark score. Entries that are greater than 0 mean that a given density forecast is more accurate (has a higher score) than the ARSV baseline. The numbers in parentheses are the pvalues of two-sided t-statistics for tests of equality of average log-scores. The two panels of Table 3 refer to the periods 1985, quarter 1?011, quarter 3, and 1985, quarter 1?008, quarter 2. The main findings are as follows. First, including stochastic volatility in a model considerably improves its average log-score. This is true for both the AR model and our BMF nowcasting models. Consider, for example, the small BMF model in month 2 of quarter t. The constant volatility version of the model yields an average score that is 15.1 below the ARSV baseline, Lumicitabine web whereas the stochastic volatility version yields a score that is 8.5 above the baseline. To provide some intuition for the importance of allowing time varying volatility, Fig. 2 reports the estimates of stochastic volatility from an AR model and our large BMFSV nowcasting model, obtained from the full sample of data available in our last realtime data vintage. The volatility plotted is 0:5 from equation (2), m = 1, 2, 3, corresponding to the standard deviation m,t of shocks to GDP growth in each model. For the ARSV model, we report just the posterior median of 0:5 ; for the BMFSV model, we report the posterior median and the 70 credible set. m,t The charts show that time variation in volatility is considerable for an AR model, reflecting the `Great Modera.Ll model involves as many as 14 regressors) and large BMF models. The former are slightly better when the sample ends in 2008; the latter over the full sample, suggesting that more information became relevant during the crisis. We have also experimented (in Carriero et al. (2013)) with different subgroups of the indicators. Perhaps the most interesting finding is that financial indicators, by themselves, do poorly in forecasting current quarter GDP growth. However, in line with the comparison of results across samples that was mentioned above, including financial indicators with other indicators helps the models (a little) during the recent crisis. Finally, rolling estimation of the BMF models with constant volatilities generates systematically higher RMSEs than recursive estimation of the same models. This finding suggests that the efficiency losses from using a smaller set of observations are larger than the gains from achieving partial robustness to possible breaks. The main message that we can take from the point forecast evaluation is that overall our BMF method is superior to AR model forecasts and comparable with survey forecasts, though the surveys performed a little better during the crisis. However, a major advantage of our approach is that it also easily delivers density and interval forecasts, and, as we shall now see, in this context the stochastic volatility specification that we adopt becomes quite relevant.Realtime Nowcasting5.3. Density forecasts: average predictive scores To assess the calibration of density forecasts, Table 3 provides average log-score comparisons of our BMF and BMFSV nowcasting models, taking an ARSV model as the benchmark (since previous research has shown that stochastic volatility improves density accuracy of AR forecasts). To facilitate comparisons, the first row of each part of Table 3 provides the average log-score of the ARSV forecast; the remaining rows provide the score of each other model forecast less the benchmark score. Entries that are greater than 0 mean that a given density forecast is more accurate (has a higher score) than the ARSV baseline. The numbers in parentheses are the pvalues of two-sided t-statistics for tests of equality of average log-scores. The two panels of Table 3 refer to the periods 1985, quarter 1?011, quarter 3, and 1985, quarter 1?008, quarter 2. The main findings are as follows. First, including stochastic volatility in a model considerably improves its average log-score. This is true for both the AR model and our BMF nowcasting models. Consider, for example, the small BMF model in month 2 of quarter t. The constant volatility version of the model yields an average score that is 15.1 below the ARSV baseline, whereas the stochastic volatility version yields a score that is 8.5 above the baseline. To provide some intuition for the importance of allowing time varying volatility, Fig. 2 reports the estimates of stochastic volatility from an AR model and our large BMFSV nowcasting model, obtained from the full sample of data available in our last realtime data vintage. The volatility plotted is 0:5 from equation (2), m = 1, 2, 3, corresponding to the standard deviation m,t of shocks to GDP growth in each model. For the ARSV model, we report just the posterior median of 0:5 ; for the BMFSV model, we report the posterior median and the 70 credible set. m,t The charts show that time variation in volatility is considerable for an AR model, reflecting the `Great Modera.
