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Time-varying Combinations of Predictive Densities using Nonlinear Filtering

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Author Info

  • Monica Billio

    (University of Venice, GRETA Assoc. and School for Advanced Studies in Venice)

  • Roberto Casarin

    (University of Venice, GRETA Assoc. and School for Advanced Studies in Venice)

  • Francesco Ravazzolo

    (Norges Bank and BI Norwegian Business School)

  • Herman K. van Dijk

    (Erasmus University Rotterdam, VU University Amsterdam)

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 instability 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-118/III.

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Date of creation: 07 Nov 2012
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Handle: RePEc:dgr:uvatin:20120118

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Web page: http://www.tinbergen.nl

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. Roberto Casarin & Stefano Grassi & Francesco Ravazzolo & Harman K. van Dijk, 2014. "Parallel sequential Monte Carlo for efficient density combination: The DeCo MATLAB toolbox," Working Paper, Norges Bank 2014/11, Norges Bank.
  2. Marco J. Lombardi & Francesco Ravazzolo, 2012. "Oil price density forecasts: exploring the linkages with stock markets," Working Paper, Norges Bank 2012/24, Norges Bank.
  3. Fawcett, Nicholas & Kapetanios, George & Mitchell, James & Price, Simon, 2014. "Generalised density forecast combinations," Bank of England working papers 492, Bank of England.
  4. 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 Paper, Norges Bank 2013/20, Norges Bank.
  5. Anne Opschoor, 2014. "Improving Density Forecasts and Value-at-Risk Estimates by Combining Densities," Tinbergen Institute Discussion Papers 14-090/III, Tinbergen Institute.
  6. 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.
  7. Nalan Basturk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute.
  8. Marco Jacopo Lombardi, 2013. "On the correlation between commodity and equity returns: implications for portfolio allocation," BIS Working Papers 420, Bank for International Settlements.
  9. 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.

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