期刊名称：Discussion Papers in Economics / Department of Economics, University of York
出版年度：2014
卷号：2014
出版社：University of York
摘要：In this paper, we consider a specification testing problem in nonlinear time series models with nonstationary regressors and propose using a nonparametric kernel-based test statistic. The nullasymptotics for the proposed nonparametric test statistic have been well developed in the existing literature such as Gao et al (2009b) and Wang and Phillips (2012). In this paper, we study the local asymptotics of the test statistic, i.e., the asymptotic properties of the test statistic under a sequence of general nonparametric local alternatives, and show that the asymptotic distribution depends on the asymptotic behaviour of the distance function which is the local deviation from the parametrically specified model in the null hypothesis. In order to implement the proposed test in practice, we introduce a bootstrap procedure to approximate the critical values of the test statistic and establish a novel result of Edgeworth expansion which is used to justify the use of such an approximation. Based on the approximate critical values, we develop a bandwidth selection method, which chooses the optimal bandwidth that maximises the local power of the test while its size is controlled at a given significance level. The local power is defined as the power of the proposed test for a given sequence of local alternatives. Such a bandwidth selection is made feasible by an approximate expression for the local power of the test as a function of the bandwidth. A Monte-Carlo simulation study is provided to illustrate the finite sample performance of the proposed test.
关键词：Asymptotic distribution; Edgeworth expansion; local power function; nonlinear time series; quadratic form; size function; specification testing; unit root.
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