2011/11/01 by Michael H. Neumann
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #math.ST #stat.TH
paper · pdf · doi:10.3150/10-bej313
published as Bernoulli 2011, Vol. 17, No. 4, 1268-1284 · Published in at http://dx.doi.org/10.3150/10-BEJ313 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2011/11/01 · arxiv created 2012/01/05 · arxiv updated 2012/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.