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arXiv · 1610.03215

Specification testing in nonparametric AR-ARCH models

Marie Hušková·Natalie Neumeyer·Tobias Niebuhr·Leonie Selk
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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. A test for the model assumption of independence of innovations from past time series values is suggested. The test is based on an weighted $L^2$-distance of empirical characteristic functions. The asymptotic distribution under the null hypothesis of independence is derived and consistency against fixed alternatives is shown. A smooth autoregressive residual bootstrap procedure is suggested and its performance is shown in a simulation study.

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Marie Hušková, Natalie Neumeyer, Tobias Niebuhr, Leonie Selk. 2016-10-11. Specification testing in nonparametric AR-ARCH models. https://arxiv.org/abs/1610.03215

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