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Specification testing in nonparametric AR-ARCH models. (English) Zbl 1417.62247

Authors’ 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 Cramèr-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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference

Software:

RMetrics; timeSeries; R
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Full Text: DOI arXiv

References:

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