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2022 | OriginalPaper | Buchkapitel

Asymptotics of Alternative Interdependence Measures for Bivariate \(\alpha -\)Stable Autoregressive Model of Order 1

verfasst von : Aleksandra Grzesiek, Agnieszka Wyłomańska

Erschienen in: Nonstationary Systems: Theory and Applications

Verlag: Springer International Publishing

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Abstract

In this paper, we concentrate on the two-dimensional \(\alpha \)-stable autoregressive model of order 1. For this model, we analyze the auto-dependence functions applied to describe the interdependence of the time series components considered separately as the one-dimensional processes. Since the classical second moment-based dependence measures are not defined in the \(\alpha -\)stable case, we examine here the auto-codifference and the auto-covariation functions. The main result of this paper is the derivation of the formulas which describe the asymptotics of the considered measures of interdependence. The theoretical results are supported by a simulation study.

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Metadaten
Titel
Asymptotics of Alternative Interdependence Measures for Bivariate Stable Autoregressive Model of Order 1
verfasst von
Aleksandra Grzesiek
Agnieszka Wyłomańska
Copyright-Jahr
2022
DOI
https://doi.org/10.1007/978-3-030-82110-4_3

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