Goodness-of-fit testing of error distribution in nonparametric ARCH(1) models

Hira L. Koul and Xiaoqing Zhu

Journal of Multivariate Analysis, 2015, vol. 137, issue C, 141-160

Abstract: This paper discusses the goodness-of-fit testing of an error distribution in a nonparametric autoregressive conditionally heteroscedastic model of order one. The test is based on a weighted empirical distribution function of the residuals, where the residuals are obtained from a local linear fit for the autoregressive and heteroscedasticity functions, and the weights are chosen to adjust for the undesirable behavior of these nonparametric estimators in the tails of their domains. An asymptotically distribution free test is obtained via the Khmaladze martingale transformation. A simulation study is included to assess the finite sample level and power behavior of this test. It exhibits some superiority of this test compared to the classical Kolmogorov–Smirnov and Cramér–von Mises tests in terms of the finite sample level and power.

Keywords: Khmaladze martingale transform test; Singular incomplete information matrix (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:137:y:2015:i:c:p:141-160

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DOI: 10.1016/j.jmva.2015.02.009

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