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Bayesian forecast combination for VAR models

Author

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  • Andersson, Michael K

    () (Monetary Policy Department, Central Bank of Sweden)

  • Karlsson, Sune

    () (Department of Business, Economics, Statistics and Informatics)

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

  • Andersson, Michael K & Karlsson, Sune, 2007. "Bayesian forecast combination for VAR models," Working Paper Series 216, Sveriges Riksbank (Central Bank of Sweden).
  • Handle: RePEc:hhs:rbnkwp:0216
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    References listed on IDEAS

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    1. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    2. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    3. Bernanke, Ben S. & Boivin, Jean, 2003. "Monetary policy in a data-rich environment," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 525-546, April.
    4. Jana Eklund & Sune Karlsson, 2007. "Forecast Combination and Model Averaging Using Predictive Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 329-363.
    5. Kapetanios, George & Labhard, Vincent & Price, Simon, 2008. "Forecast combination and the Bank of England's suite of statistical forecasting models," Economic Modelling, Elsevier, vol. 25(4), pages 772-792, July.
    6. John G. Galbraith & Greg Tkacz, 2006. "How Far Can We Forecast? Forecast Content Horizons For Some Important Macroeconomic Time Series," Departmental Working Papers 2006-13, McGill University, Department of Economics.
    7. Kadiyala, K Rao & Karlsson, Sune, 1997. "Numerical Methods for Estimation and Inference in Bayesian VAR-Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 99-132, March-Apr.
    8. Gary Koop & Simon Potter, 2004. "Forecasting in dynamic factor models using Bayesian model averaging," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 550-565, December.
    9. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    10. Sune Karlsson & Tor Jacobson, 2004. "Finding good predictors for inflation: a Bayesian model averaging approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 479-496.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Mehmet Balcilar & Rangan Gupta & Anandamayee Majumdar & Stephen M. Miller, 2012. "Was the Recent Downturn in US GDP Predictable?," Working Papers 201230, University of Pretoria, Department of Economics.
    4. Gary Koop, 2012. "Using VARs and TVP-VARs with Many Macroeconomic Variables," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(3), pages 143-167, September.
    5. 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.
    6. Francesco Ravazzolo & Shaun P Vahey, 2010. "Measuring Core Inflation in Australia with Disaggregate Ensembles," RBA Annual Conference Volume,in: Renée Fry & Callum Jones & Christopher Kent (ed.), Inflation in an Era of Relative Price Shocks Reserve Bank of Australia.
    7. 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.
    8. Wolters, Maik H., 2011. "Forecasting under Model Uncertainty," Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48723, Verein für Socialpolitik / German Economic Association.
    9. Ida Wolden Bache & James Mitchell & Francesco Ravazzolo & Shaun P. Vahey, 2009. "Macro modelling with many models," Working Paper 2009/15, Norges Bank.
    10. David Jamieson Bolder & Yuliya Romanyuk, 2008. "Combining Canadian Interest-Rate Forecasts," Staff Working Papers 08-34, Bank of Canada.
    11. Hugo Gerard & Kristoffer Nimark, 2008. "Combining Multivariate Density Forecasts Using Predictive Criteria," RBA Research Discussion Papers rdp2008-02, Reserve Bank of Australia.
    12. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    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. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, Elsevier.
    15. 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.
    16. Korobilis, Dimitris, 2008. "Forecasting in vector autoregressions with many predictors," MPRA Paper 21122, University Library of Munich, Germany.
    17. 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.
    18. Jakub Ryšánek, 2010. "Combining VAR Forecast Densities Using Fast Fourier Transform," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2010(5), pages 72-88.

    More about this item

    Keywords

    Bayesian model averaging; Predictive likelihood; GDP forecasts;

    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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