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Persistence probabilities for MA(1) sequences with uniform innovations
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Persistence probabilities for MA(1) sequences with uniform innovations
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We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions, characterized by the location of the uniform distribution and the coupling parameter of the process, where the persistence probabilities have qualitatively different behaviour. We obtain the generating functions of the persistence probabilities explicitly in all possible regions. In some of the regions, the persistence probabilities can be expressed explicitly in terms of various combinatorial quantities.
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MA(1) processes with uniform innovations conditioned to stay positive in the non-expanding regime
An MA(1) process with uniform innovations conditioned to stay positive converges to an explicit Doob h-transform with phase-dependent transition kernel when the coupling parameter lies in [-1,1).
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