Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 630-638.

• Articles • Previous Articles     Next Articles

Diagnostic Checking for Multivariate GARCH-type Models in Time Series

1 WU Jian-Hong, 2ZHU Li-XIng   

  1. 1.School of Statistics and Mathematics, Zhejiang Gongshang University,  Hangzhou 310018;
    2.Department of Mathematics,  |Hong Kong Baptist University, Hong Kong
  • Received:2008-12-11 Revised:2009-12-23 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    香港研究资助局项目、中国教育部人文社科项目(07JJD790154)、浙江省自然科学基金(Y6090172)以及浙江工商大学青年人才基金资助

Abstract:

Multiple time series with time-varying conditional variance are verified to be useful in both theory and real applications. In this article, a battery of score-type diagnostic tests are suggested for checking the adequacy of multivariate GARCH-type models fitting multiple time series. The
resulting tests are asymptotically chi-squared under the null hypothesis, and critical values can  be obtained easily. Moreover, they are sensitive to alternatives and  can detect the alternatives approaching the null at the rate arbitrarily close to 1/√n,  the fastest possible rate in goodness-of-fit test. For a large number of alternatives, an asymptotically distribution-free maximin test is constructed. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. Furthermore, it is worthwhile to show that the battery of tests can detect separate aspects of possible departures from the null and then provide us more specifical information about the likely source of misspecification. Simulation results indicate that the tests perform well.

Key words: GARCH-type models, Maximin test, Model diagnostic checking,  Score type test

CLC Number: 

  • 62F05
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