Specification testing in nonparametric AR‐ARCH models

Marie Hušková, Natalie Neumeyer, Tobias Niebuhr and Leonie Selk

Scandinavian Journal of Statistics, 2019, vol. 46, issue 1, 26-58

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 L2‐distances of empirical characteristic functions are considered as well as a Cramér–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.

Date: 2019
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https://doi.org/10.1111/sjos.12337

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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:46:y:2019:i:1:p:26-58

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