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Bayesian forecast combination for VAR models

In: Bayesian Econometrics

Author

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  • Michael K. Andersson
  • Sune Karlsson

Abstract

We consider forecast combination and, indirectly, model selection for VAR models when there is uncertainty about which variables to include in the model in addition to the forecast variables. The key difference from traditional Bayesian variable selection is that we also allow for uncertainty regarding which endogenous variables to include in the model. That is, all models include the forecast variables, but may otherwise have differing sets of endogenous variables. This is a difficult problem to tackle with a traditional Bayesian approach. Our solution is to focus on the forecasting performance for the variables of interest and we construct model weights from the predictive likelihood of the forecast variables. The procedure is evaluated in a small simulation study and found to perform competitively in applications to real world data.

Suggested Citation

  • Michael K. Andersson & Sune Karlsson, 2008. "Bayesian forecast combination for VAR models," Advances in Econometrics, in: Bayesian Econometrics, pages 501-524, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-9053(08)23015-x
    DOI: 10.1016/S0731-9053(08)23015-X
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    Cited by:

    1. is not listed on IDEAS
    2. Maik H. Wolters, 2015. "Evaluating Point and Density Forecasts of DSGE Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 74-96, January.
    3. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    4. Mirriam Chitalu Chama-Chiliba & Rangan Gupta & Nonophile Nkambule & Naomi Tlotlego, 2011. "Forecasting Key Macroeconomic Variables of the South African Economy Using Bayesian Variable Selection," Working Papers 201132, University of Pretoria, Department of Economics.
    5. Gary Koop, 2012. "Using VARs and TVP-VARs with Many Macroeconomic Variables," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(3), pages 143-167, September.
    6. Korobilis, Dimitris & Pettenuzzo, Davide, 2019. "Adaptive hierarchical priors for high-dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 212(1), pages 241-271.
    7. Jochmann, Markus & Koop, Gary & Strachan, Rodney W., 2010. "Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks," International Journal of Forecasting, Elsevier, vol. 26(2), pages 326-347, April.
    8. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    9. Tomáš Jeřábek & Radka Šperková, 2015. "A Predictive Likelihood Approach to Bayesian Averaging," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 63(4), pages 1269-1276.
    10. Jakub Ryšánek, 2010. "Combining VAR Forecast Densities Using Fast Fourier Transform," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2010(5), pages 72-88.
    11. Francesco Ravazzolo & Shaun P Vahey, 2010. "Measuring Core Inflation in Australia with Disaggregate Ensembles," RBA Annual Conference Volume (Discontinued), in: Renée Fry & Callum Jones & Christopher Kent (ed.),Inflation in an Era of Relative Price Shocks, Reserve Bank of Australia.
    12. Mehmet Balcilar & Rangan Gupta & Anandamayee Majumdar & Stephen M. Miller, 2012. "Was the Recent Downturn in US GDP Predictable?," Working Papers 1210, University of Nevada, Las Vegas , Department of Economics.
    13. James H. Stock & Mark W. Watson, 2012. "Generalized Shrinkage Methods for Forecasting Using Many Predictors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 481-493, June.
    14. Hugo Gerard & Kristoffer Nimark, 2008. "Combining multivariate density forecasts using predictive criteria," Economics Working Papers 1117, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2008.
    15. Anders Warne & Günter Coenen & Kai Christoffel, 2017. "Marginalized Predictive Likelihood Comparisons of Linear Gaussian State‐Space Models with Applications to DSGE, DSGE‐VAR, and VAR Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 103-119, January.
    16. David Jamieson Bolder & Yuliya Romanyuk, 2010. "Combining Canadian Interest Rate Forecasts," Palgrave Macmillan Books, in: Arjan B. Berkelaar & Joachim Coche & Ken Nyholm (ed.), Interest Rate Models, Asset Allocation and Quantitative Techniques for Central Banks and Sovereign Wealth Funds, chapter 1, pages 3-30, Palgrave Macmillan.
    17. Dimitris Korobilis, 2008. "Forecasting in vector autoregressions with many predictors," Advances in Econometrics, in: Bayesian Econometrics, pages 403-431, Emerald Group Publishing Limited.
    18. Hilde C. Bjørnland & Karsten Gerdrup & Anne Sofie Jore & Christie Smith & Leif Anders Thorsrud, 2012. "Does Forecast Combination Improve Norges Bank Inflation Forecasts?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(2), pages 163-179, April.
    19. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    20. Dr. James Mitchell, 2009. "Macro Modelling with Many Models," National Institute of Economic and Social Research (NIESR) Discussion Papers 337, National Institute of Economic and Social Research.

    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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