Time-Varying Combinations of Predictive Densities Using Nonlinear Filtering

Tinbergen Institute Discussion Paper 12-118/III

54 Pages Posted: 8 Nov 2012  

Monica Billio

Ca Foscari University of Venice - Dipartimento di Economia

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics

Francesco Ravazzolo

Free University of Bolzano

H. K. van Dijk

Tinbergen Institute; Econometric Institute

Date Written: October 29, 2012

Abstract

We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models can be individually misspecified. A Sequential Monte Carlo method is proposed to approximate the filtering and predictive densities. The combination approach is assessed using statistical and utility-based performance measures for evaluating density forecasts. Simulation results indicate that, for a set of linear autoregressive models, the combination strategy is successful in selecting, with probability close to one, the true model when the model set is complete and it is able to detect parameter i nstability when the model set includes the true model that has generated subsamples of data. For the macro series we find that incompleteness of the models is relatively large in the 70's, the beginning of the 80's and during the recent financial crisis, and lower during the Great Moderation. With respect to returns of the S&P 500 series, we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 90's and switches to giving more weight to the professional forecasts over time.

Keywords: Density Forecast Combination, Survey Forecast, Bayesian Filtering, Sequential Monte Carlo

JEL Classification: C11, C15, C53, E37

Suggested Citation

Billio, Monica and Casarin, Roberto and Ravazzolo, Francesco and van Dijk, H. K., Time-Varying Combinations of Predictive Densities Using Nonlinear Filtering (October 29, 2012). Tinbergen Institute Discussion Paper 12-118/III. Available at SSRN: https://ssrn.com/abstract=2172254 or http://dx.doi.org/10.2139/ssrn.2172254

Monica Billio (Contact Author)

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

HOME PAGE: http://venus.unive.it/billio

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics ( email )

San Giobbe 873/b
Venice, 30121
Italy
+39 030.298.91.49 (Phone)
+39 030.298.88.37 (Fax)

HOME PAGE: http://venus.unive.it/r.casarin/

Francesco Ravazzolo

Free University of Bolzano ( email )

Bolzano
Italy

Herman K. Van Dijk

Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 4088955 (Phone)
+31 10 4527746 (Fax)

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Burg. Oudlaan 50
Amsterdam/Rotterdam, 1082 MS
Netherlands
+31104088955 (Phone)
+31104089031 (Fax)

HOME PAGE: http://people.few.eur.nl/hkvandijk/

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