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Estimation And Asymptotic Theory For A New Class Of Mixture Models

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Author Info

  • Eduardo Mendes

    (Department of Electrical Engineering, PUC-Rio)

  • Alvaro Veiga

    (Department of Electrical Engineering, PUC-Rio)

  • MArcelo Cunha Medeiros

    ()
    (Department of Economics, PUC-Rio)

Abstract

In this paper a new model of mixture of distributions is proposed, where the mixing structure is determined by a smooth transition tree architecture. Models based on mixture of distributions are useful in order to approximate unknown conditional distributions of multivariate data. The tree structure yields a model that is simpler, and in some cases more interpretable, than previous proposals in the literature. Based on the Expectation-Maximization (EM) algorithm a quasi-maximum likelihood estimator is derived and its asymptotic properties are derived under mild regularity conditions. In addition, a specific-to-general model building strategy is proposed in order to avoid possible identification problems. Both the estimation procedure and the model building strategy are evaluated in a Monte Carlo experiment, which give strong support for the theory developed in small samples. The approximation capabilities of the model is also analyzed in a simulation experiment. Finally, two applications with real datasets are considered. KEYWORDS: Mixture models, smooth transition, EM algorithm, asymptotic properties, time series, conditional distribution.

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Bibliographic Info

Paper provided by Department of Economics PUC-Rio (Brazil) in its series Textos para discussão with number 538.

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Length: 33p
Date of creation: Jan 2007
Date of revision:
Handle: RePEc:rio:texdis:538

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  1. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
  2. van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999. "A simple variable selection technique for nonlinear models," Working Paper Series in Economics and Finance 296, Stockholm School of Economics, revised 06 Apr 2000.
  4. Wolfgang HÄRDLE & H. LÜTKEPOHL & R. CHEN, 1996. "A Review of Nonparametric Time Series Analysis," SFB 373 Discussion Papers 1996,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  6. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  7. da Rosa, Joel Correa & Veiga, Alvaro & Medeiros, Marcelo C., 2008. "Tree-structured smooth transition regression models," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2469-2488, January.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  9. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  10. Medeiros, Marcelo C. & Teräsvirta, Timo & Rech, Gianluigi, 2002. "Building neural network models for time series: A statistical approach," Working Paper Series in Economics and Finance 508, Stockholm School of Economics.
  11. Medeiros, Marcelo & Veiga, Alvaro, 2000. "A Flexible Coefficient Smooth Transition Time Series Model," Working Paper Series in Economics and Finance 360, Stockholm School of Economics, revised 10 Feb 2000.
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