Absolute regularity and ergodicity of Poisson count processes

by    M. H. Neumann

Preprint series: 10-09, Reports on Stochastics and Statistics

M. H. Neumann

Preprint series: , Reports on Stochastics and Statistics

MSC:
60G10 Stationary processes
37A25 Ergodicity, mixing, rates of mixing
62M07 Non-Markovian processes: hypothesis testing

Abstract: We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that the stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.

Keywords: Absolute regularity, ergodicity, integer-valued process, mixing, Poisson count process, test.

Upload: 2010-08-12

Update: 2010 -08 -12


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