Absolute regularity and ergodicity of Poisson count processes

Details Absolute regularity and ergodicity of Poisson count processes Absolute regularity and ergodicity of Poisson count processes

2012-01-05

arxiv.org/abs/1201.1071v1

Bernoulli 2011, Vol. 17, No. 4, 1268-1284

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ313 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ313

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 a 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.

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