SYSTEMATIC APPROACH FOR PORTMANTEAU TESTS IN VIEW OF THE WHITTLE LIKELIHOOD RATIO
スポンサーリンク
概要
- 論文の詳細を見る
Box and Pierce (1970) proposed a test statistic <var>TBP</var> which is the squared sum of <var>m</var> sample autocorrelations of the estimated residual process of an autoregressive-moving average model of order (p,q). <var>TBP</var> 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 <var>TBP</var> is approximated by a chi-square distribution with (m-p-q) degrees of freedom, ``if <var>m</var> is moderately large". This paper shows that <var>TBP</var> is understood to be a special form of the Whittle likelihood ratio test <var>TPW</var> for autoregressive-moving average spectral density with <var>m</var>-dependent residual processes. Then, it is shown that, for any finite <var>m</var>, <var>TPW</var> does not converge to a chi-square distribution with (m-p-q) degrees of freedom in distribution, and that if we assume Bloomfields exponential spectral density, <var>TPW</var> is asymptotically chi-square distributed for any finite <var>m</var>. From this observation we propose a modified <var>TPW</var> which is asymptotically chi-square distributed. In view of the likelihood ratio, we also mention the asymptotics of a natural Whittle likelihood ratio test <var>TWLR</var> which is always asymptotically chi-square distributed. Its local power is also evaluated. Numerical studies illuminate interesting features of <var>TPW</var>, <var>TPW</var>, and <var>TWLR</var>. 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.
- 2009-12-01
著者
-
Amano Tomoyuki
Department Of Applied Mathematics School Of Science And Engineering Waseda University
-
Amano Tomoyuki
Department Of Applied Mathematics School Of Fundamental Science And Engineering Waseda University
-
Taniguchi Masanobu
Department Of Applied Mathematics School Of Science And Engineering Waseda University
-
Taniguchi Masanobu
Department Of Applied Mathematics School Of Fundamental Science And Engineering Waseda University
関連論文
- ASYMPTOTIC EFFICIENCY OF ESTIMATING FUNCTION ESTIMATORS FOR NONLINEAR TIME SERIES MODELS
- SYSTEMATIC APPROACH FOR PORTMANTEAU TESTS IN VIEW OF THE WHITTLE LIKELIHOOD RATIO
- GENERALIZED INFORMATION CRITERIA IN MODEL SELECTION FOR LOCALLY STATIONARY PROCESSES(CELEBRATION VOLUME FOR AKAIKE)
- COMPARISON OF WHITTLE TYPE PORTMANTEAU TESTS
- NOTE ON ASYMPTOTICS OF WHITTLE ESTIMATORS FOR SQUARE TRANSFORMED ARCH(∞) MODELS
- DYNAMIC PORTFOLIO OPTIMIZATION USING GENERALIZED DYNAMIC CONDITIONAL HETEROSKEDASTIC FACTOR MODELS
- RANK-BASED INFERENCE FOR MULTIVARIATE NONLINEAR AND LONG-MEMORY TIME SERIES MODELS
- AN ESTIMATION METHOD IN TIME SERIES ERRORS-IN-VARIABLES MODELS
- GENERALIZED INFORMATION CRITERIA IN MODEL SELECTION FOR LOCALLY STATIONARY PROCESSES
- GENERALIZED INFORMATION CRITERIA IN MODEL SELECTION FOR LOCALLY STATIONARY PROCESSES