2012/11/06 by Leonie Selk, Natalie Neumeyer, Selk, Leonie +1
Decision Sciences · Mathematics · #62G05 #62G10 #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #Methodology (stat.ME) #Primary 62M10 #Secondary 62G30 #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1211.1212
openalex publication_date 2012/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a nonparametric autoregression model under conditional\nheteroscedasticity with the aim to test whether the innovation distribution\nchanges in time. To this end we develop an asymptotic expansion for the\nsequential empirical process of nonparametrically estimated innovations\n(residuals). We suggest a Kolmogorov-Smirnov statistic based on the difference\nof the estimated innovation distributions built from the first ns and the last\nn-ns residuals, respectively. Weak convergence of the underlying stochastic\nprocess to a Gaussian process is proved under the null hypothesis of no change\npoint. The result implies that the test is asymptotically distribution-free.\nConsistency against fixed alternatives is shown. The small sample performances\nof the proposed test is investigated in a simulation study and the test is\napplied to data examples.\n