We are glad to invite you to the following seminar
When: September 16th, 2014, 11:00 am
Where: epartment of Management, Economics and quantitative Methods, Via dei Caniana n. 2 – Room 15
Title: Unified View of Portmanteau Tests for General Statistical Models
Speacker: Masanobu TANIGUCHI Department of Applied Mathematics School of Science and Engineering Waseda University of Tokyo, Japan
Abstract: This talk consists of the two parts (I) and (II). (I) Systematic Approach for Portmanteau Tests in View of Whittle Likelihood Ratio: Box and Pierce (1970) proposed a test statistic TBP which is the squared sum of m sample autocorrelations of the estimated residual process of autoregressive moving average model of order (p,q). TBP 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 TBP is approximated by chi-square distribution with (m-p-q) degrees of freedom, ”if m is moderately large”. This paper shows that TBP is understood as a special form of Whittle likelihood ratio test TPW for autoregressive-moving average spectral density with m-dependent residual process. Then, it is shown that, for any finite m, TPW does not converge to chi-square distribution with (m-p-q) degrees of freedom in distribution, and that, if we assume Bloomfield’s exponential spectral density TPW is asymptotically chi-square distributed for any finite m. From this observation we propose a natural Whittle likelihood ratio test TWLR which is always asymptotically chi-square distributed. Its local power is also evaluated. Numerical studies illuminate interesting features of TWLR. Because many versions of the portmanteau test have been proposed, and been used in variety of fields, our systematic approach for portmanteau tests and proposal of TWLR will give a unified view and useful applications. (II) A Unified View of Portmanteau Test for Diagnostic Checking : Here we construct a portmanteau test statistic TP as a sort of the likelihood ratio test for general statistical models based on the procedure given in (I). Then we derive sufficient conditions that the statistic is asymptotically chi-square distributed. Furthermore, it is shown that if a time series model whose spectral density has a product structure satisfies appropriate conditions, TP is asymptotically chi-square distributed. We also introduce a useful application of the test for variable selection. (Joint work with Tomoyuki AMANO and Hiroaki Odashima)
For further information please contact: ilia.negri@unibg.it or marida.bertocchi@unibg.it
Ilia Negri http://www.unibg.it/pers/?ilia.negri