Random self-decomposability and autoregressive processes

Tomasz J. Kozubowski and Krzysztof Podgórski

Statistics & Probability Letters, 2010, vol. 80, issue 21-22, 1606-1611

Abstract: We introduce the notion of random self-decomposability and discuss its relation to the concepts of self-decomposability and geometric infinite divisibility. We present its connection with time series autoregressive schemes with a regression coefficient that randomly turns on and off. In particular, we provide a characterization of random self-decomposability as well as that of marginal distributions of stationary time series that follow this scheme. Our results settle an open question related to the existence of such processes.

Keywords: Geometric; infinite; divisibility; Geometric; stable; law; Laplace; distribution; Linnik; distribution; Non-Gaussian; time; series (search for similar items in EconPapers)
Date: 2010
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