Constancy and Goodness of Fit Test for Time Series Models

Abstract

In this thesis, we concentrate on the constancy test of parameter and goodness of fit test for time series models. For the constancy test, we consider two cusum type test procedures to detect parameter change. The first one is cusum type retrospective test to detect parameter change in the past given observations and the other one is cusum type sequential test that sequentially monitor the constancy of parameters based on historical sample. First, we apply the cusum type retrospective test to various time series model and investigate their limiting distribution. We derive its limiting null distribution and report a simulation result that validates our test. Second, we apply a monitoring procedure to detect change of the parameter in random coefficient model. Moreover, we develop a monitoring procedure to detect change of the copula parameter in strong mixing processes. We propose two monitoring procedures based on the cumulative sums of scores and the fluctuations of copula parameter estimates. Further, we investigate the asymptotic properties of our monitoring procedures under both the null of no change in the copula parameter and its alternative. We also illustrate a simulation study and a real data analysis. Finally, for goodness of fit test, we consider the maximum entropy test. We apply this test to GARCH model and AR(∞) model. Its asymptotic distribution is derived under the null hypothesis. Through a simulation study, it is demonstrated that the proposed test performs adequately. Particularly, a bootstrap method is employed to cope with small samples. We also conduct a real data analysis for illustration.