Time-varying combinations of predictive densities using nonlinear filtering

Billio, Monica; Casarin, Roberto; Ravazzolo, Francesco; Dijk, Herman K. van

doi:10.1016/j.jeconom.2013.04.009

Cited by 138 publications

(77 citation statements)

References 71 publications

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“…We recommend as a further exciting and stimulating research line the use of consistent scoring functions for model combination and/or model calibration with the aim of improving on Mitchell and Hall (), Hall and Mitchell (), Geweke and Amisano (, ), Billio et al . () and Fawcett et al . ().…”

Section: Discussion On the Paper By Ehm Gneiting Jordan And Krügermentioning

confidence: 87%

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Ehm

Gneiting

Jordan³

et al. 2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

147

205

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Summary. In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional. For example, forecasters might be asked to report the mean or a quantile of their predictive distributions. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be consistent for the functional at hand, in the sense that the expected score is minimized when following the directive. We show that any scoring function that is consistent for a quantile or an expectile functional can be represented as a mixture of elementary or extremal scoring functions that form a linearly parameterized family. Scoring functions for the mean value and probability forecasts of binary events constitute important examples. The extremal scoring functions admit appealing economic interpretations of quantiles and expectiles in the context of betting and investment problems. The Choquet-type mixture representations give rise to simple checks of whether a forecast dominates another in the sense that it is preferable under any consistent scoring function. In empirical settings it suffices to compare the average scores for only a finite number of extremal elements. Plots of the average scores with respect to the extremal scoring functions, which we call Murphy diagrams, permit detailed comparisons of the relative merits of competing forecasts.

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Section: Discussion On the Paper By Ehm Gneiting Jordan And Krügermentioning

confidence: 87%

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Ehm

Gneiting

Jordan³

et al. 2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

147

205

View full text Add to dashboard Cite

show abstract

“…Billio et al . () obtain superior financial forecasts by combining model‐based and survey‐based densities, using time‐varying weights derived from a distributional state space representation.…”

Section: Quantile Aggregation and Other Density Forecast Combinationsmentioning

confidence: 99%

“…More recently, time‐varying density combination weights have been considered, showing that they can lead to forecast improvements (see e.g. Waggoner and Zha, ; Billio et al ., ; Kapetanios et al ., ; Del Negro, Hasegawa and Schorfheide, ).…”

Section: Introductionmentioning

confidence: 99%

Quantile Aggregation of Density Forecasts

Busetti

2017

Oxf Bull Econ Stat

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Quantile aggregation (or ‘Vincentization’) is a simple and intuitive way of combining probability distributions, originally proposed by S.B. Vincent in 1912. In certain cases, such as under Gaussianity, the Vincentized distribution belongs to the same family as that of the individual distributions and it can be obtained by averaging the individual parameters. This article compares the properties of quantile aggregation with those of the forecast combination schemes normally adopted in the econometric forecasting literature, based on linear or logarithmic averages of the individual densities. Analytical results and Monte Carlo experiments indicate that the properties of quantile aggregation are between those of the linear and the logarithmic pool. Larger differences among the combination schemes occur when there are biases in the individual forecasts: in that case quantile aggregation seems preferable on the whole. The practical usefulness of Vincentization is illustrated empirically in the context of linear forecasting models for Italian GDP and quantile predictions of euro area inflation.

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“…Hall and Mitchell (2007) and Geweke and Amisano (2010) propose using combination schemes based on the Kullback-Leibler score; Gneiting and Raftery (2007) recommend strictly proper scoring rules, such as the cumulative rank probability score, in particular, if the focus is on some particular area, such as extreme tails, of the distribution. Billio et al (2013) (hereby BCRVD 2013) provide a general Bayesian distributional state space representation of predictive densities and specify combination schemes that allow for an incomplete set of models and different learning mechanisms and scoring rules.…”

Section: Introductionmentioning

confidence: 99%

Parallel Sequential Monte Carlo for Efficient Density Combination: TheDeCoMATLABToolbox

Casarin¹,

Grassi²,

Ravazzolo³

et al. 2015

J. Stat. Soft.

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This paper presents the MATLAB package DeCo (density combination) which is based on the paper by Billio, Casarin, Ravazzolo, and van Dijk (2013) where a constructive Bayesian approach is presented for combining predictive densities originating from different models or other sources of information. The combination weights are time-varying and may depend on past predictive forecasting performances and other learning mechanisms. The core algorithm is the function DeCo which applies banks of parallel sequential Monte Carlo algorithms to filter the time-varying combination weights. The DeCo procedure has been implemented both for standard CPU computing and for graphical process unit (GPU) parallel computing. For the GPU implementation we use the MATLAB parallel computing toolbox and show how to use general purpose GPU computing almost effortlessly. This GPU implementation provides a speed-up of the execution time of up to seventy times on a standard CPU MATLAB implementation on a multicore CPU. We show the use of the package and the computational gain of the GPU version through some simulation experiments and empirical applications.

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Time-varying combinations of predictive densities using nonlinear filtering

Cited by 138 publications

References 71 publications

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Quantile Aggregation of Density Forecasts

Parallel Sequential Monte Carlo for Efficient Density Combination: TheDeCoMATLABToolbox

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