Subsampling Ratio Tests For Structural Changes In Time Series With Heavy-tailed AR(p) Errors

The change-point problem was the first to extract from the quality control problem.The problem of testing for structural changes covers a broad variety of real-world fields such as economics,clinical science,and engineering.If the parameters change without consideration,the prediction and statistical inference will be invalid,so it has subsequently been an essential and interesting issue to test for the structural change point.Recently,the ratio type test statistic has become a popular method to detect change points in time series,because it does not need to be standardized by any variance estimate.In fact,lots of literature have concentrated on the observations with finite variance.However,much of empirical work has shown that the heavy-tailed phenomenon exists frequently,and the information is in the tail and can not be characterized by traditional Gaussian sequences,so it makes sense to consider infinite variance sequences.In addition,it is more general to consider the weakly dependent case,such as AR(p)process.Therefore,it is of great significance to combine two key factors of the heavy tailness and dependence of random variables to study the structural changes in time series.We consider that issues related to the mean of heavy-tailed AR(p)series are possibly subject to change at most once at some unknown point in time and a ratio statistic is constructed to test whether unknown changes have occurred.It is shown that asymptotic distribution of this test statistic under the no-change null hypothesis is functional for Levy process and its consistency is given under the alternative.To avoid the nuisance parameter,we provide a Subsampling method that returns more accurate critical values for this test.The validity of the Subsampling,algorithm is proved.A simulation study shows the Subsampling ratio test achieves the correct sizes and comparable powers in large samples.Researchers have proposed some estimators to analyze changes in trend,but there has been little discussion on how detecting these change points.We consider that issues related to the trend of heavy-tailed AR(p)series may occur at most one change at some unknown point in time.It is shown that asymptotic distribution of this test statistic under the no-change null hypothesis is functional for Levy process and its consistency is given under the alternative.A simulation study shows the Subsampling ratio test achieves the correct sizes and comparable powers in large samples.Further,we consider two sets of the stock price data of British Petroleum and Google.These two empirical examples indicate that Subsampling ratio tests are effective and feasible to detect structural changes in time series with heavy-tailed AR(p)errors.