IDEAS home Printed from https://ideas.repec.org/p/rba/rbardp/rdp2008-02.html
   My bibliography  Save this paper

Combining Multivariate Density Forecasts Using Predictive Criteria

Author

Listed:
  • Hugo Gerard

    (Reserve Bank of Australia)

  • Kristoffer Nimark

    (Reserve Bank of Australia)

Abstract

This paper combines multivariate density forecasts of output growth, inflation and interest rates from a suite of models. An out-of-sample weighting scheme based on the predictive likelihood as proposed by Eklund and Karlsson (2007) and Andersson and Karlsson (2007) is used to combine the models. Three classes of models are considered: a Bayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR) and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australian data over the inflation-targeting period, we find that, at short forecast horizons, the Bayesian VAR model is assigned the most weight, while at intermediate and longer horizons the factor model is preferred. The DSGE model is assigned little weight at all horizons, a result that can be attributed to the DSGE model producing density forecasts that are very wide when compared with the actual distribution of observations. While a density forecast evaluation exercise reveals little formal evidence that the optimally combined densities are superior to those from the best-performing individual model, or a simple equal-weighting scheme, this may be a result of the short sample available.

Suggested Citation

  • Hugo Gerard & Kristoffer Nimark, 2008. "Combining Multivariate Density Forecasts Using Predictive Criteria," RBA Research Discussion Papers rdp2008-02, Reserve Bank of Australia.
    • Handle: RePEc:rba:rbardp:rdp2008-02
    as

    Download full text from publisher

    File URL: https://www.rba.gov.au/publications/rdp/2008/pdf/rdp2008-02.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    3. 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.
    4. Adolfson, Malin & Laseen, Stefan & Linde, Jesper & Villani, Mattias, 2007. "Bayesian estimation of an open economy DSGE model with incomplete pass-through," Journal of International Economics, Elsevier, vol. 72(2), pages 481-511, July.
    5. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    6. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    7. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    8. Kapetanios, George & Labhard, Vincent & Price, Simon, 2008. "Forecasting Using Bayesian and Information-Theoretic Model Averaging: An Application to U.K. Inflation," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 33-41, January.
    9. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
    10. Frank Smets & Raf Wouters, 2004. "Forecasting with a Bayesian DSGE Model: An Application to the Euro Area," Journal of Common Market Studies, Wiley Blackwell, vol. 42(4), pages 841-867, November.
    11. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    12. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    13. 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.
    14. Jean Boivin & Serena Ng, 2005. "Understanding and Comparing Factor-Based Forecasts," International Journal of Central Banking, International Journal of Central Banking, vol. 1(3), December.
    15. Christian Gillitzer & Jonathan Kearns, 2007. "Forecasting with Factors: The Accuracy of Timeliness," RBA Research Discussion Papers rdp2007-03, Reserve Bank of Australia.
    16. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    17. 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.
    18. Litterman, Robert, 1986. "Forecasting with Bayesian vector autoregressions -- Five years of experience : Robert B. Litterman, Journal of Business and Economic Statistics 4 (1986) 25-38," International Journal of Forecasting, Elsevier, vol. 2(4), pages 497-498.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. David Norman & Anthony Richards, 2012. "The Forecasting Performance of Single Equation Models of Inflation," The Economic Record, The Economic Society of Australia, vol. 88(280), pages 64-78, March.
    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. Kirdan Lees, 2009. "Overview of a recent Reserve Bank workshop: nowcasting with model combination," Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 72, pages 31-33, March.
    4. Bjørnland, Hilde C. & Gerdrup, Karsten & Jore, Anne Sofie & Smith, Christie & Thorsrud, Leif Anders, 2011. "Weights and pools for a Norwegian density combination," The North American Journal of Economics and Finance, Elsevier, vol. 22(1), pages 61-76, January.
    5. Bekiros Stelios & Paccagnini Alessia, 2015. "Estimating point and density forecasts for the US economy with a factor-augmented vector autoregressive DSGE model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(2), pages 107-136, April.
    6. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    7. Valeriu Nalban, 2015. "Do Bayesian Vector Autoregressive models improve density forecasting accuracy? The case of the Czech Republic and Romania," International Journal of Economic Sciences, International Institute of Social and Economic Sciences, vol. 4(1), pages 60-74, March.
    8. 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.
    9. 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.
    10. Cardani, Roberta & Paccagnini, Alessia & Villa, Stefania, 2019. "Forecasting with instabilities: An application to DSGE models with financial frictions," Journal of Macroeconomics, Elsevier, vol. 61(C), pages 1-1.
    11. Knotek, Edward S. & Zaman, Saeed, 2023. "Real-time density nowcasts of US inflation: A model combination approach," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1736-1760.
    12. James Bishop & Peter Tulip, 2017. "Anticipatory Monetary Policy and the 'Price Puzzle'," RBA Research Discussion Papers rdp2017-02, Reserve Bank of Australia.
    13. Ida Wolden Bache & James Mitchell & Francesco Ravazzolo & Shaun P. Vahey, 2009. "Macro modelling with many models," Working Paper 2009/15, Norges Bank.
    14. Farooq Akram & Andrew Binning & Junior Maih, 2016. "Joint Prediction Bands for Macroeconomic Risk Management," Working Papers No 5/2016, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    15. Sean Langcake & Tim Robinson, 2013. "An Empirical BVAR-DSGE Model of the Australian Economy," RBA Research Discussion Papers rdp2013-07, Reserve Bank of Australia.
    16. 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.
    17. Peter Tulip & Stephanie Wallace, 2012. "Estimates of Uncertainty around the RBA's Forecasts," RBA Research Discussion Papers rdp2012-07, Reserve Bank of Australia.
    18. Reif Magnus, 2021. "Macroeconomic uncertainty and forecasting macroeconomic aggregates," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-20, April.
    19. Andrew Hodge & Tim Robinson & Robyn Stuart, 2008. "A Small BVAR-DSGE Model for Forecasting the Australian Economy," RBA Research Discussion Papers rdp2008-04, Reserve Bank of Australia.
    20. Roberta Cardani & Alessia Paccagnini & Stefania Villa, 2015. "Forecasting in a DSGE Model with Banking Intermediation: Evidence from the US," Working Papers 292, University of Milano-Bicocca, Department of Economics, revised Feb 2015.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Berg, Tim O. & Henzel, Steffen R., 2015. "Point and density forecasts for the euro area using Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1067-1095.
    2. Bekiros Stelios & Paccagnini Alessia, 2015. "Estimating point and density forecasts for the US economy with a factor-augmented vector autoregressive DSGE model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(2), pages 107-136, April.
    3. 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.
    4. 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.
    5. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.
    6. Stelios D. Bekiros & Alessia Paccagnini, 2016. "Policy‐Oriented Macroeconomic Forecasting with Hybrid DGSE and Time‐Varying Parameter VAR Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(7), pages 613-632, November.
    7. Bekiros, Stelios D. & Paccagnini, Alessia, 2014. "Bayesian forecasting with small and medium scale factor-augmented vector autoregressive DSGE models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 298-323.
    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. Knut Are Aastveit & Francesco Ravazzolo & Herman K. van Dijk, 2018. "Combined Density Nowcasting in an Uncertain Economic Environment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 131-145, January.
    10. Adolfson, Malin & Lindé, Jesper & Villani, Mattias, 2005. "Forecasting Performance of an Open Economy Dynamic Stochastic General Equilibrium Model," Working Paper Series 190, Sveriges Riksbank (Central Bank of Sweden), revised 01 Jun 2006.
    11. 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.
    12. Rangan Gupta & Marius Jurgilas & Alain Kabundi & Stephen M. Miller, 2009. "Monetary Policy and Housing Sector Dynamics in a Large-Scale Bayesian Vector Autoregressive Model," Working Papers 200913, University of Pretoria, Department of Economics.
    13. 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.
    14. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    15. Rangan Gupta & Stephen M. Miller & Dylan van Wyk, 2010. "Financial Market Liberalization, Monetary Policy, and Housing Price Dynamics," Working papers 2010-06, University of Connecticut, Department of Economics.
    16. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    17. Gupta, Rangan & Kabundi, Alain & Miller, Stephen M., 2011. "Forecasting the US real house price index: Structural and non-structural models with and without fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 2013-2021, July.
    18. Knut Are Aastveit & Karsten R. Gerdrup & Anne Sofie Jore & Leif Anders Thorsrud, 2014. "Nowcasting GDP in Real Time: A Density Combination Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 48-68, January.
    19. Pär Österholm, 2009. "Incorporating Judgement in Fan Charts," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(2), pages 387-415, June.
    20. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2022. "The global component of inflation volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 700-721, June.

    More about this item

    Keywords

    density forecasts; combining forecasts; predictive criteria;
    All these keywords.

    JEL classification:

    • 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rba:rbardp:rdp2008-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Paula Drew (email available below). General contact details of provider: https://edirc.repec.org/data/rbagvau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.