Abstract
In this paper we derive an explicit formula for the expected value of the first time a ℤ+-valued AR(1) process exceeds a given level. Using martingale theory we obtain a generalized Wald's equation that holds under a simple integrability condition. As an application, we give an asymptotic formula for the expected value of the first exit time of the AR(1) process with a thinned Poisson innovation.
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Aly, EE.A.A., Bouzar, N. On the First Entry Time of a ℤ+-valued AR(1) Process. Annals of the Institute of Statistical Mathematics 51, 359–367 (1999). https://doi.org/10.1023/A:1003870427536
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DOI: https://doi.org/10.1023/A:1003870427536