Inference and testing for structural change in time series of counts model
vendredi 12 avril 2013, 9h30 - 10h30
We consider inference and change-point problem in Poisson autoregression with infinitely many lags. The conditional mean of the process is involved as a non-linear function of it past values and the past observations. Under some Lipschitz-type conditions, it is shown that the conditional mean can be written as a function of lagged observations. For this latter model, we assume that the link function depends on an unknown parameter $\theta_0$. The consistency and the asymptotic normality of the maximum likelihood estimator of the parameter are proved. These results are used to study change-point problem in the parameter $\theta_0$. We propose two tests based on the likelihood of the observations. Under the null hypothesis of no change, it is shown that each of these test statistics converges to a well know distribution. The consistency under the alternative is established. Some results of an empirical study are provided.