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Limit Theorems for Moving Averages with Random Coefficients and Heavy-Tailed Noise

Part of: Distribution theory - Probability Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Rafał Kulik
Rafał Kulik*
Affiliation:
University of Wrocław and University of Ottawa
*
∗ Postal address: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada. Email address: rkuli438@science.uottawa.ca
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Abstract

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We consider a stationary moving average process with random coefficients, , generated by an array, {Ct,k, t ∈ Z, k ≥ 0}, of random variables and a heavy-tailed sequence, {Zt, t ∈ Z}. We analyze the limit behavior using a point process analysis. As applications of our results we compare the limiting behavior of the moving average process with random coefficients with that of a standard MA(∞) process.

Keywords

Nonlinear processpoint processself-normalized sum

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60G10: Stationary processes 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 245 - 256
Copyright
© Applied Probability Trust 2006 

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