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Autoregressive processes with normal-Laplace marginals

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  • Jose, K.K.
  • Tomy, Lishamol
  • Sreekumar, J.

Abstract

The normal-Laplace distribution introduced by Reed and Jorgensen [Reed, W.J., Jorgensen, M., 2004. The double Pareto-lognormal distribution, A new parametric model for size distributions. Comm. Statist-Theory and Methods, 33, 1733-1753], is studied briefly. A first order autoregressive process with normal-Laplace stationary marginal distribution is introduced and various properties are discussed. The process gives a combination of Gaussian as well as non-Gaussian time series models for the first time and is free from the zero defect problem. Simulation studies are done and sample path properties are explored. Regression behaviour of the process is studied. The applications in modelling data from various contexts are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2456-2462
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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. 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.
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    7. Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
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    1. 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.
    2. Halvarsson, Daniel, 2013. "On the Estimation of Skewed Geometric Stable Distributions," Ratio Working Papers 216, The Ratio Institute.
    3. Kozubowski, Tomasz J. & Podgórski, Krzysztof, 2010. "Random self-decomposability and autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1606-1611, November.
    4. Tomy, Lishamol & Jose, K.K., 2009. "Generalized normal-Laplace AR process," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1615-1620, July.
    5. Alice B. V. Mello & Maria C. S. Lima & Abraão D. C. Nascimento, 2022. "A notable Gamma‐Lindley first‐order autoregressive process: An application to hydrological data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.

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