多元时间序列GARCH型模型的诊断检验

多元时间序列GARCH型模型已被证实在理论和实际中具有重要作用.该文对这一类模型的拟合优度提出了一组得分型检验统计量.这些检验在零假设模型下渐近服从卡方分布,计算简单,临界值容易得到.检验对备择模型比较敏感,能侦察到以1/n~(1/2)的速度收敛到零假设的备择模型.对于可能的多个备择,构造了渐近分布自由的Maximin检验;而对于饱和备择情形,基于得分型检验的思想提出了一个构造Omnibus检验的可能性.值得指出的是构造的这组检验能检测到零假设模型的条件协差阵的每一部分可能的偏离,从而当模型被错误指定时,该检验能提供相关信息进行模型修正.模拟结果表明该文的检验表现理想.

Diagnostic Checking for Multivariate GARCH-type Models in Time Series

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. Theresulting 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.