A test for parameter change in general causal time series using quasi-likelihood estimator

William Charky Kengne (1)

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

In this paper, we propose a new procedure to test a change in the parameter of a process $ X= (X_t)_{t\in \Z}$ belonging to a class of causal models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models. Two statistics $\widehat{Q}^{(1)}_n$ and $ \widehat{Q}^{(2)}_n$ are constructed using the quasi-likelihood estimator (QMLE) of the parameter. Under the null hypothesis that there is no change, each of these statistics converges weakly to a well-known distribution and the maximum diverges to infinity under the alternative of one change. Some simulation results are reported.

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

William Charky Kengne. A test for parameter change in general causal time series using quasi-likelihood estimator. Comptes Rendus. Mathématique, 2012, 350, pp.307-312. ⟨10.1016/j.crma.2012.03.001⟩. ⟨hal-00793222⟩