Ratio Test for Mean Changes in Time Series with Heavy-Tailed AR(p) Noise Based on Multiple Sampling Methods

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distribution of the modified statistic is a functional of Levy processes and the consistency under the alternative hypothesis is obtained. However, a heavy-tailed index exists in the asymptotic distribution and is difficult to estimate. This paper uses bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, and obtain more accurate critical values and empirical power. In addition, some results from a small simulation study and a practical example give an idea of the finite sample behavior of the proposed statistic.

Automated summary

This paper discusses the problem of mean changes in time series with heavy-tailed AR(p) noise and proposes a modified ratio-type test statistic. By using bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, more accurate critical values and empirical power are obtained. Some results from a small simulation study and a practical example further validate the effectiveness of the proposed statistic.