Premium
Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach
Author(s) -
Selk Leonie,
Neumeyer Natalie
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12030
Subject(s) - mathematics , heteroscedasticity , nonparametric statistics , autoregressive model , asymptotic distribution , econometrics , test statistic , weak convergence , consistency (knowledge bases) , statistic , null hypothesis , gaussian process , statistics , statistical hypothesis testing , empirical distribution function , gaussian , computer science , physics , geometry , computer security , quantum mechanics , estimator , asset (computer security)
We consider a nonparametric autoregression model under conditional heteroscedasticity with the aim to test whether the innovation distribution changes in time. To this end, we develop an asymptotic expansion for the sequential empirical process of nonparametrically estimated innovations (residuals). We suggest a Kolmogorov–Smirnov statistic based on the difference of the estimated innovation distributions built from the first ⌊ ns ⌋and the last n − ⌊ ns ⌋ residuals, respectively (0 ≤ s ≤ 1). Weak convergence of the underlying stochastic process to a Gaussian process is proved under the null hypothesis of no change point. The result implies that the test is asymptotically distribution‐free. Consistency against fixed alternatives is shown. The small sample performance of the proposed test is investigated in a simulation study and the test is applied to a data example.