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Ergodicity and existence of moments for local mixtures of linear autoregressions

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  • Carvalho, Alexandre
  • Skoulakis, Georgios
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    Abstract

    We consider a class of nonlinear time series expressed as a local mixture of a finite number of linear autoregressions. The mixing weights are continuous functions of lagged observations while the densities of the innovation terms in each autoregression can be very general and are only assumed to possess finite moments of some order. We focus on the probabilistic properties of the model and provide mild sufficient conditions for geometric ergodicity and existence of moments.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 4 (March)
    Pages: 313-322

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:313-322

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    Related research

    Keywords: Nonlinear time series Autoregressions Mixture models Markov chains Geometric ergodic Uniformly geometric ergodic Invariant measure;

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    1. LeBaron, Blake, 1992. "Some Relations between Volatility and Serial Correlations in Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 65(2), pages 199-219, April.
    2. Markku Lanne & Pentti Saikkonen, 2003. "Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 96-125.
    3. An, Hongzhi & Chen, Min & Huang, Fuchun, 1997. "The geometric ergodicity and existence of moments for a class of non-linear time series model," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 213-224, January.
    4. Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.
    5. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, April.
    6. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
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