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Mixtures of nonparametric autoregressions

Author

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  • J. Franke
  • J.-P. Stockis
  • J. Tadjuidje-Kamgaing
  • W. Li

Abstract

We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterising the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.

Suggested Citation

  • J. Franke & J.-P. Stockis & J. Tadjuidje-Kamgaing & W. Li, 2011. "Mixtures of nonparametric autoregressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 287-303.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:287-303
    DOI: 10.1080/10485252.2010.539686
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    References listed on IDEAS

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    1. Jean‐Pierre Stockis & Jürgen Franke & Joseph Tadjuidje Kamgaing, 2010. "On geometric ergodicity of CHARME models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 141-152, May.
    2. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
    3. Stockis, Jean-Pierre & Tadjuidje-Kamgaing, Joseph & Franke, Jürgen, 2008. "A note on the identifiability of the conditional expectation for the mixtures of neural networks," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 739-742, April.
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    Cited by:

    1. Arash Nademi & Rahman Farnoosh, 2014. "Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 275-293, February.
    2. Mark Fiecas & Jürgen Franke & Rainer von Sachs & Joseph Tadjuidje Kamgaing, 2017. "Shrinkage Estimation for Multivariate Hidden Markov Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 424-435, January.
    3. Nademi, Arash & Nademi, Younes, 2018. "Forecasting crude oil prices by a semiparametric Markov switching model: OPEC, WTI, and Brent cases," Energy Economics, Elsevier, vol. 74(C), pages 757-766.
    4. Lisandro Javier Fermin & Ricardo Rios & Luis Angel Rodriguez, 2017. "A Robbins–Monro Algorithm for Non-Parametric Estimation of NAR Process with Markov Switching: Consistency," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 809-837, November.

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