[Forum SIS] Taniguchi's seminar at Bergamo University

[Ilia Negri]

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 a unibg.it or
marida.bertocchi a unibg.it

Ilia Negri
http://www.unibg.it/pers/?ilia.negri
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