1. Random self-decomposability and autoregressive processes
- Author
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Kozubowski, Tomasz J. and Podgórski, Krzysztof
- Subjects
- *
AUTOREGRESSION (Statistics) , *GEOMETRIC analysis , *DISTRIBUTION (Probability theory) , *GAUSSIAN processes , *TIME series analysis , *MATHEMATICAL decomposition , *EXISTENCE theorems - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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