English

A note on nonparametric testing for Gaussian innovations in AR-ARCH models

Methodology 2012-11-07 v1

Abstract

In this paper we consider autoregressive models with conditional autoregressive variance, including the case of homoscedastic AR-models and the case of ARCH models. Our aim is to test the hypothesis of normality for the innovations in a completely nonparametric way, i. e. without imposing parametric assumptions on the conditional mean and volatility functions. To this end the Cram\'er-von Mises test based on the empirical distribution function of nonparametrically estimated residuals is shown to be asymptotically distribution-free. We demonstrate its good performance for finite sample sizes in a simulation study.

Cite

@article{arxiv.1211.1204,
  title  = {A note on nonparametric testing for Gaussian innovations in AR-ARCH models},
  author = {Natalie Neumeyer and Leonie Selk},
  journal= {arXiv preprint arXiv:1211.1204},
  year   = {2012}
}
R2 v1 2026-06-21T22:33:37.624Z