Abstract：In this paper， the problem of the mean change point test of the p-order autoregressive process with stable distribution is considered. By constructing the modified ratio test statistic and using the generalized central limit theorem， it is proved that the asymptotic distribution of the statistic under the null hypothesis is a functional of Lévy distribution， and its consistency under the alternative hypothesis is obtained . For the case that the asymptotic distribution depends on unknown parameters， the Bootstrap sampling is used to approximate the asymptotic distribution to obtain more accurate critical values. The numerical simulation results show that the ratio test based on Bootstrap sampling not only controls the empirical sizes well， but also the empirical powers achieves satisfactory results. In addition， when the mutation position is located in the second half of the sample， the empirical powers is greatly improved. Finally， a set of Alcoa's closing prices further verifies the validity and feasibility of the change point test method proposed in this paper.
2023, Vol. 57 
