Random self-decomposability and autoregressive processes |
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Authors: | Tomasz J Kozubowski Krzysztof Podgórski |
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Institution: | 1. Department of Mathematics and Statistics, University of Nevada, Reno NV 89557, USA;2. Department of Mathematical Statistics, Lund University, SE-221 00 Lund, Sweden |
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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. |
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