Publication at Faculty of Mathematics and Physics |
2019
Abstract
In this paper, an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. Tests for the model assumption of independence of innovations from past time series values are suggested.
Tests based on weighted L-2-distances of empirical characteristic functions are considered as well as a Cramer-von Mises-type test. The asymptotic distributions under the null hypothesis of independence are derived, and the consistency against fixed alternatives is shown.
A smooth autoregressive residual bootstrap procedure is suggested, and its performance is shown in a simulation study.