文章基本信息

标题：Systematic Approach for Portmanteau Tests in View of the Whittle Likelihood Ratio
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作者：Masanobu Taniguchi ; Tomoyuki Amano
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2009
卷号：39
期号：2
页码：177-192
DOI：10.14490/jjss.39.177
出版社：JAPAN STATISTICAL SOCIETY
摘要：Box and Pierce (1970) proposed a test statistic T_BP which is the squared sum of m sample autocorrelations of the estimated residual process of an autoregressive-moving average model of order (p,q). T_BP is called the classical portmanteau test. Under the null hypothesis that the autoregressive-moving average model of order (p,q) is adequate, they suggested that the distribution of T_BP is approximated by a chi-square distribution with (m-p-q) degrees of freedom, ``if m is moderately large". This paper shows that T_BP is understood to be a special form of the Whittle likelihood ratio test T_PW for autoregressive-moving average spectral density with m -dependent residual processes. Then, it is shown that, for any finite m , T_PW does not converge to a chi-square distribution with (m-p-q) degrees of freedom in distribution, and that if we assume Bloomfield's exponential spectral density, T_PW is asymptotically chi-square distributed for any finite m . From this observation we propose a modified T_PW which is asymptotically chi-square distributed. In view of the likelihood ratio, we also mention the asymptotics of a natural Whittle likelihood ratio test T_WLR which is always asymptotically chi-square distributed. Its local power is also evaluated. Numerical studies illuminate interesting features of T_PW , T_PW , and T_WLR . Because many versions of the portmanteau test have been proposed and been used in a variety of fields, our systematic approach for portmanteau tests and proposal of tests will give another view and useful applications.
关键词：ARMA model;Exponential spectral model;LAN;local power;Portmanteau test;Time series model checking;Whittle likelihood