Subsampling ratio tests for structural changes in time series with heavy-tailed AR(p) errors - Jin, Hao; Wang, Aimin; Zhang, Si; Liu, Jia (Communications in statistics. Simulation and computation, 2024)
In this article, we consider that issues related to the mean and trend of heavy-tailed AR(p) series are possibly subject to change at most once at some unknown point in time. Under the inspiration of Shao (J. Time Ser. Anal., 2011, 32, 598-606), two ratio statistics are constructed to test whether unknown changes have occurred. It is shown that asymptotic distributions of these test statistics under the no-change null hypothesis are functional for Lévy processes and their consistencies are given under the alternative. To avoid the nuisance parameter, we provide a subsampling method that returns more accurate critical values for these tests. The validity of the subsampling algorithm is proved. A simulation study shows the subsampling-based ratio tests achieve the correct empirical sizes and comparable empirical powers in large samples. Finally, two practical applications using real data set are presented.