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The modified Yule-Walker method for α-stable time series models

Author

Listed:
  • Kruczek, Piotr
  • Wyłomańska, Agnieszka
  • Teuerle, Marek
  • Gajda, Janusz

Abstract

This paper discusses the problem of parameters estimation for stable periodic autoregressive (PAR) time series. Considered models generalize popular and widely accepted autoregressive (AR) time series. By examining measures of dependence for α-stable processes, first we introduce new empirical estimator of autocovariation for α-stable sequences. Based on this approach we generalize Yule–Walker method for estimation of parameter for PAR time series. Thus we fill a gap in estimation methods for non-Gaussian models. We test proposed procedure and show its consistency. Moreover, we use our approach to model real empirical data thus showing usefulness of heavy tailed models in statistical modelling.

Suggested Citation

  • Kruczek, Piotr & Wyłomańska, Agnieszka & Teuerle, Marek & Gajda, Janusz, 2017. "The modified Yule-Walker method for α-stable time series models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 588-603.
    • Handle: RePEc:eee:phsmap:v:469:y:2017:i:c:p:588-603
    DOI: 10.1016/j.physa.2016.11.037
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    References listed on IDEAS

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    1. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, December.
    2. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
    3. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
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