A test for parameter change in general causal time series models

William Charky Kengne (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We consider a process $ X=(X_t)_{t\in\Z}$ belonging to a large class of causal models. We assume that the model depends on a parameter $\theta_0$ and consider the problem of test for change of the parameter. The test statistic is based on the quasi-maximum likelihood estimator (QLME) of the parameter. Given a significance level $\alpha\in (0,1)$, it is shown that the asymptotic size of the test less than $\alpha$. Under the local alternative that there is one change, we show that the test statistic converges almost surely to $\infty$. Some simulation results for AR(1), ARCH(1) and GARCH(1,1) models are reported.

Mots clés: Semi-parametric test; Change of parameters; Causal processes; Quasi-maximum likelihood estimator; Weak convergence.; Weak convergence

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

William Charky Kengne. A test for parameter change in general causal time series models. 2011. ⟨hal-00561015v1⟩