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Testing Gaussianity and Linearity in Multivariate Time Series and Their Applications

检验多元时间序列中的高斯性和线性及其应用

基本信息

批准号：
12630024
负责人：
TERUI Nobuhiko
金额：
$ 1.79万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

Based on a characterization of orthogonality of Gaussian random variates after Hermitian polynomials transformation, we developed a Gaussianity teat for multivariate stationary time series, where a univariate Gaussianity test proposed by Kariya, Tsay Terui and Li(1998) was extended to multivariate situation. Our simulation study showed that the proposed test has reasonable power and outperforms multivariate bispectrum test available in the literature when the innovation series of the time series is symmetric, but non-Gaussian.Testing Gaussianity is closely related to testing linearity for univariate time series analysis, because nonlinearity implies non-normality in a regular time series. Extending to multivariate situation, it does not always holdbecause of their inter-relationship between marginal series. That is, non-Gaussianity of each marginal series does not always require non-linear modeling of multivariate series as a whole. We introduced a multivariate time series model, we call multivariate time series with common non-Gaussian component, which represents the above relationship and we used the proponed test to detect it. In case of that, the proposed multivariate Gaussianity test was modified so as to decompose the omnibus teats into two orthogonal tests statistics, each of which test the Gaussianity for marginal series and the inter-relational Gaussianity respectively.Further some modification of tests was proposed to accommodate the inconsistency between marginal tests and omnibus test and we showed that it gave a useful insight of inter-relationship between marginal time series for multivariate time series with common non-Gaussian component. This reduces the burden of non-Gaussian modeling, equivalently non-linear modeling in a sense, into linear Gaussian modeling.

基于高斯随机变量经Hermitian多项式变换后的正交性的一个特征，将卡里耶，Tsay Terui和Li（1998）提出的一元高斯性检验推广到多元平稳时间序列，提出了一种多元平稳时间序列的高斯性检验方法.我们的模拟研究表明，提出的测试有合理的权力和多元双谱检验在文献中提供的时间序列的新息序列是对称的，但non-Gaussianity是密切相关的检验线性的时间序列分析，因为非线性意味着非正态性的一个规则的时间序列。扩展到多元情形，由于边际序列之间的相互关系，它并不总是成立的。也就是说，每个边际序列的非高斯性并不总是需要将多变量序列作为一个整体进行非线性建模。本文引入了一种多元时间序列模型，称之为具有共同非高斯分量的多元时间序列，它代表了上述关系，并利用提出的检验方法来检验这一关系，在此基础上，对提出的多元高斯检验方法进行了改进，将综合检验分解为两个正交检验统计量，每一个测试的高斯边际系列和内部，进一步提出了一些修正的测试，以适应边缘测试和综合测试之间的不一致，我们表明，这为研究具有共同非高斯成分的多元时间序列的边际时间序列之间的相互关系提供了有益的启示。这减少了非高斯建模的负担，在某种意义上等效于非线性建模为线性高斯建模。