A New Bispectral Test for NonLinear Serial Dependence
改进了Hinich双谱检验，通过最大化检验统计量关于平滑参数的取值，解决了原检验功效低和需要指定平滑参数的问题，蒙特卡洛模拟显示新检验功效更高且稳健。
Nonconstancy of the bispectrum of a time series has been taken as a measure of non-Gaussianity and nonlinear serial dependence in a stochastic process by Subba Rao and Gabr (1980 Subba Rao , T. , Gabr , M. ( 1980 ). A test for linearity of stationary time series analysis . J. Time Ser. Anal. 1 : 145 – 158 .[Crossref] , [Google Scholar]) and by Hinich (1982 Hinich , M. J. ( 1982 ). Testing for Gaussianity and linearity of a stationary time series . J. Time Ser. Anal. 3 : 169 – 175 .[Crossref] , [Google Scholar]), leading to Hinich's statistical test of the null hypothesis of a linear generating mechanism for a time series. Hinich's test has the advantage of focusing directly on nonlinear serial dependence—in contrast to subsequent approaches, which actually test for serial dependence of any kind (nonlinear or linear) on data which have been pre-whitened. The Hinich test tends to have low power, however, and (in common with most statistical procedures in the frequency domain) requires the specification of a smoothing or window-width parameter. In this article, we develop a modification of the Hinich bispectral test which substantially ameliorates both of these problems by the simple expedient of maximizing the test statistic over the feasible values of the smoothing parameter. Monte Carlo simulation results are presented indicating that the new test is well sized and has substantially larger power than the original Hinich test against a number of relevant alternatives; the simulations also indicate that the new test preserves the Hinich test's robustness to misspecifications in the identification of a pre-whitening model.