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

Piotr Kruczek, Agnieszka Wyłomańska, Marek Teuerle and Janusz Gajda

Physica A: Statistical Mechanics and its Applications, 2017, vol. 469, issue C, 588-603

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.

Keywords: Covariation; α-stable distribution; Estimation; Yule-Walker equations (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:469:y:2017:i:c:p:588-603

DOI: 10.1016/j.physa.2016.11.037

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