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Time-varying combinations of predictive densities using nonlinear filtering

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

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 of simulated data, US macroeconomic time series and surveys of stock market prices. 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 instability when the model set includes the true model that has generated subsamples of data. Also, substantial uncertainty appears in the weights when predictors are similar; residual uncertainty reduces when the model set is complete; and learning reduces this uncertainty. For the macro series we find that incompleteness of the models is relatively large in the 1970’s, the beginning of the 1980’s and during the recent financial crisis, and lower during the Great Moderation; the predicted probabilities of recession accurately compare with the NBER business cycle dating; model weights have substantial uncertainty attached. 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 1990’s and switches to giving more weight to the professional forecasts over time. Information on the complete predictive distribution and not just on some moments turns out to be very important, above all during turbulent times such as the recent financial crisis. More generally, the proposed distributional state space representation offers great flexibility in combining densities.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 177 (2013)
Issue (Month): 2 ()
Pages: 213-232

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Handle: RePEc:eee:econom:v:177:y:2013:i:2:p:213-232

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Density forecast combination; Survey forecast; Bayesian filtering; Sequential Monte Carlo;

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References

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Citations

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Cited by:
  1. Lukasz Gatarek & Lennart Hoogerheide & Koen Hooning & Herman K. van Dijk, 2013. "Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation," Tinbergen Institute Discussion Papers 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
  2. Fawcett, Nicholas & Kapetanios, George & Mitchell, James & Price, Simon, 2014. "Generalised density forecast combinations," Bank of England working papers 492, Bank of England.
  3. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2013. "Interactions between eurozone and US booms and busts: A Bayesian panel Markov-switching VAR model," Working Papers 2013:17, Department of Economics, University of Venice "Ca' Foscari".
  4. Joscha Beckmann & Rainer Schüssler, 2014. "Forecasting Equity Premia using Bayesian Dynamic Model Averaging," CQE Working Papers 2914, Center for Quantitative Economics (CQE), University of Muenster.
  5. Roberto Casarin & Stefano Grassi & Francesco Ravazzolo & Herman K. van Dijk, 2013. "Parallel Sequential Monte Carlo for Efficient Density Combination: The DeCo Matlab Toolbox," Working Papers 2013:08, Department of Economics, University of Venice "Ca' Foscari".
  6. Marco J. Lombardi & Francesco Ravazzolo, 2012. "Oil price density forecasts: exploring the linkages with stock markets," Working Paper 2012/24, Norges Bank.
  7. Marco Jacopo Lombardi, 2013. "On the correlation between commodity and equity returns: implications for portfolio allocation," BIS Working Papers 420, Bank for International Settlements.

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