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Random self-decomposability and autoregressive processes

Author

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  • Kozubowski, Tomasz J.
  • Podgórski, Krzysztof

Abstract

We introduce the notion of random self-decomposability and discuss its relation to the concepts of self-decomposability and geometric infinite divisibility. We present its connection with time series autoregressive schemes with a regression coefficient that randomly turns on and off. In particular, we provide a characterization of random self-decomposability as well as that of marginal distributions of stationary time series that follow this scheme. Our results settle an open question related to the existence of such processes.

Suggested Citation

  • Kozubowski, Tomasz J. & Podgórski, Krzysztof, 2010. "Random self-decomposability and autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1606-1611, November.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:21-22:p:1606-1611
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    References listed on IDEAS

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    1. V. Lekshmi & K. Jose, 2004. "An autoregressive process with geometric α-laplace marginals," Statistical Papers, Springer, vol. 45(3), pages 337-350, July.
    2. Tomy, Lishamol & Jose, K.K., 2009. "Generalized normal-Laplace AR process," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1615-1620, July.
    3. Lekshmi, V. Seetha & Jose, K.K., 2006. "Autoregressive processes with Pakes and geometric Pakes generalized Linnik marginals," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 318-326, February.
    4. A. J. Lawrance & P. A. W. Lewis, 1982. "A Mixed Exponential Time Series Model," Management Science, INFORMS, vol. 28(9), pages 1045-1053, September.
    5. Jayakumar, K. & Kuttykrishnan, A.P., 2007. "A time-series model using asymmetric Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1636-1640, October.
    6. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.
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