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Hierarchical Markov normal mixture models with applications to financial asset returns

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  • Amisano, Gianni
  • Geweke, John

Abstract

With the aim of constructing predictive distributions for daily returns, we introduce a new Markov normal mixture model in which the components are themselves normal mixtures. We derive the restrictions on the autocovariances and linear representation of integer powers of the time series in terms of the number of components in the mixture and the roots of the Markov process. We use the model prior predictive distribution to study its implications for some interesting functions of returns. We apply the model to construct predictive distributions of daily S&P500; returns, dollarpound returns, and one- and ten-year bonds. We compare the performance of the model with ARCH and stochastic volatility models using predictive likelihoods. The model's performance is about the same as its competitors for the bond returns, better than its competitors for the S&P 500 returns, and much better for the dollar-pound returns. Validation exercises identify some potential improvements. JEL Classification: C53, G12, C11, C14

Suggested Citation

  • Amisano, Gianni & Geweke, John, 2007. "Hierarchical Markov normal mixture models with applications to financial asset returns," Working Paper Series 831, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:2007831
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    Cited by:

    1. Joshua C.C. Chan & Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2012. "Time Varying Dimension Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 358-367, January.
    2. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    3. Koop, Gary & Korobilis, Dimitris, 2011. "UK macroeconomic forecasting with many predictors: Which models forecast best and when do they do so?," Economic Modelling, Elsevier, vol. 28(5), pages 2307-2318, September.
    4. Çakmaklı, Cem & Paap, Richard & van Dijk, Dick, 2013. "Measuring and predicting heterogeneous recessions," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2195-2216.
    5. Martin Meier & Enrico Minelli & Herakles Polemarchakis, 2014. "Competitive markets with private information on both sides," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 257-280, February.
    6. Monica Billio & Roberto Casarin, 2010. "Bayesian Estimation of Stochastic-Transition Markov-Switching Models for Business Cycle Analysis," Working Papers 1002, University of Brescia, Department of Economics.
    7. Amisano, Gianni & Geweke, John, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series 969, European Central Bank.
    8. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    9. Rosella Levaggi & Francesco Menoncin, 2009. "Decentralized provision of merit and impure public goods," Working Papers 0909, University of Brescia, Department of Economics.
    10. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    11. 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.
    12. Bisin, A. & Geanakoplos, J.D. & Gottardi, P. & Minelli, E. & Polemarchakis, H., 2011. "Markets and contracts," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 279-288.
    13. Francesco Menoncin & Paolo Panteghini, 2009. "Retrospective Capital Gains Taxation in the Real World," CESifo Working Paper Series 2674, CESifo Group Munich.
    14. Jushan Bai & Peng Wang, 2011. "Conditional Markov chain and its application in economic time series analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 715-734, August.
    15. Del Boca, Alessandra & Fratianni, Michele & Spinelli, Franco & Trecroci, Carmine, 2010. "The Phillips curve and the Italian lira, 1861-1998," The North American Journal of Economics and Finance, Elsevier, vol. 21(2), pages 182-197, August.
    16. Bin Chen & Yongmiao Hong, 2013. "A Unified Approach to Validating Univariate and Multivariate Conditional Distribution Models in Time Series," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    17. Yin-Wong Cheung & Sang-Kuck Chung, 2011. "A Long Memory Model with Normal Mixture GARCH," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 517-539, November.
    18. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    19. Alessandro Fedele & Paolo M. Panteghini & Sergio Vergalli, 2011. "Optimal Investment and Financial Strategies under Tax‐Rate Uncertainty," German Economic Review, Verein für Socialpolitik, vol. 12(4), pages 438-468, November.
    20. Amedeo Fossati & Rosella Levaggi, 2008. "Delay is not the answer: waiting time in health care & income redistribution," Working Papers 0801, University of Brescia, Department of Economics.
    21. repec:rim:rimwps:22-08 is not listed on IDEAS
    22. Xianguo Huang & Roberto Leon-Gonzalez & Somrasri Yupho, 2012. "Financial Integration from a Time-Varying Cointegration Perspective," GRIPS Discussion Papers 12-07, National Graduate Institute for Policy Studies.
    23. Alessandro Fedele & Raffaele Miniaci, 2010. "Do Social Enterprises Finance Their Investments Differently from For-profit Firms? The Case of Social Residential Services in Italy," Journal of Social Entrepreneurship, Taylor & Francis Journals, vol. 1(2), pages 174-189, October.
    24. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    25. Alessandro Fedele & Francesco Liucci & Andrea Mantovani, 2009. "Credit availability in the crisis: the European investment bank group," Working Papers 0913, University of Brescia, Department of Economics.

    More about this item

    Keywords

    Asset returns; Bayesian; forecasting; MCMC; mixture models;

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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