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A method for fitting stable autoregressive models using the autocovariation function

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  • Gallagher, Colin M.

Abstract

We use the sample covariations to estimate the parameters in a univariate symmetric stable autoregressive process. Unlike the sample correlation, the sample covariation can be used to estimate the tail decay parameter of the process. The fitted model will be consistent with the dependence as measured by the covariation. The limit distribution of the sample covariation can be used to derive confidence intervals for the autoregressive parameter in a first order process. Simulations show that confidence intervals coming from the covariation have better coverage probabilities than those coming from the sample correlations. The method is demonstrated on a time series of sea surface temperatures.

Suggested Citation

  • Gallagher, Colin M., 2001. "A method for fitting stable autoregressive models using the autocovariation function," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 381-390, July.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:4:p:381-390
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    Citations

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    Cited by:

    1. Aastha M. Sathe & N. S. Upadhye, 2019. "Estimation of the Parameters of Symmetric Stable ARMA and ARMA-GARCH Models," Papers 1911.09985, arXiv.org.
    2. Bielak, Łukasz & Grzesiek, Aleksandra & Janczura, Joanna & Wyłomańska, Agnieszka, 2021. "Market risk factors analysis for an international mining company. Multi-dimensional, heavy-tailed-based modelling," Resources Policy, Elsevier, vol. 74(C).
    3. Andrews, Beth & Davis, Richard A., 2013. "Model identification for infinite variance autoregressive processes," Journal of Econometrics, Elsevier, vol. 172(2), pages 222-234.
    4. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    5. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.
    6. Serttas, Fatma Ozgu, 2010. "Essays on infinite-variance stable errors and robust estimation procedures," ISU General Staff Papers 201001010800002742, Iowa State University, Department of Economics.

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