Comparing Density Forecasts via Weighted Likelihood Ratio Tests

Amisano, Gianni; Giacomini, Raffaella

doi:10.1198/073500106000000332

“…Like Amisano and Giacomini (2007) and Hall and Mitchell (2007), we use the logarithmic score to measure density fit for each component model through the evaluation period. The logarithmic scoring rule gives a high score to a density forecast that assigns a high probability to the realized value.…”

Section: Recursive Weights (Rw)mentioning

confidence: 99%

Real-time inflation forecast densities from ensemble Phillips curves

Garratt

¹

,

Mitchell

²

,

Vahey

³

et al. 2011

The North American Journal of Economics and Finance

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A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock and Watson (2004) and Clark and McCracken (2009). In this paper, we examine the effectiveness of recursive-weight and equal-weight combination strategies for density forecasting using a time-varying Phillips curve relationship between inflation and the output gap. The densities reflect the uncertainty across a large number of models using many statistical measures of the output gap, allowing for a single structural break of unknown timing. We use real-time data for the US, Australia, New Zealand and Norway. Our main finding is that the recursive-weight strategy performs well across the real-time data sets, consistently giving well-calibrated forecast densities. The equal-weight strategy generates poorly-calibrated forecast densities for the US and Australian samples. There is little difference between the two strategies for our New Zealand and Norwegian data. We also find that the ensemble modeling approach performs more consistently with real-time data than with revised data in all four countries.

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“…, J; P denotes the maximum number of lags in inflation and the output gap measures respectively, and h is the forecast horizon. 1 Notice that there is model uncertainty over the output gap measure but also the appropriate values of P (treated as fixed here). We therefore will have N different models i = 1, .…”

Section: Component Modelsmentioning

confidence: 99%

Real-Time Inflation Forecast Densities from Ensemble Phillips Curves

Garratt

¹

,

Mitchell

²

,

Vahey

³

et al. 2010

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A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock and Watson (2004) and Clark and McCracken (2009). In this paper, we examine the effectiveness of recursive-weight and equal-weight combination strategies for density forecasting using a time-varying Phillips curve relationship between inflation and the output gap. The densities reflect the uncertainty across a large number of models using many statistical measures of the output gap, allowing for a single structural break of unknown timing. We use real-time data for the US, Australia, New Zealand and Norway. Our main finding is that the recursive-weight strategy performs well across the real-time data sets, consistently giving well-calibrated forecast densities. The equal-weight strategy generates poorly-calibrated forecast densities for the US and Australian samples. There is little difference between the two strategies for our New Zealand and Norwegian data. We also find that the ensemble modeling approach performs more consistently with real-time data than with revised data in all four countries.

show abstract

“…This setup is almost identical to Giacomini and White (2006) and Amisano and Giacomini (2007). The main difference is that we are interested in a vector of path forecasts across multiple variables rather than a single variable / horizon at a time.…”

Section: A Path Forecast Accuracy Likelihood Ratio Testmentioning

confidence: 99%

“…Unlike in Amisano and Giacomini (2007) where the density, f (·), is chosen by the forecaster, here the density is specified as the loss function and is the same across forecasters.…”

Section: A Path Forecast Accuracy Likelihood Ratio Testmentioning

confidence: 99%