Ratio Test For Variance Change Point In Linear Process

A new test statistic is proposed to solve the problem that the power of the existing ratio test for the variance change point in the linear process is too low.At the same time,the asymptotic distribution under the null hypothesis and the asymptotic property under the alternative hypothesis of the statistic are studied.In addition,a new method of change point estimation is proposed,and the convergence and convergence rate of that method are established.The Monte Carlo simulation shows that the statistic has better empirical sizes and higher powers than the original statistic when the sample size is moderate,and the estimation method proposed in this paper is also consistent.To illustrate this problem,we apply our test to the series of sunspot number.Then the ratio statistic is used to test the problem of variance change point in the linear process with long memory.The asymptotic distribution under the null hypothesis and the consistence of the test under the alternative hypothesis are derived when the mean is known and the mean is unknown.In addition,a new method of change point estimation is proposed,and the convergence and convergence speed of that method are established.The simulation results show that when the variance changes from large to small,the statistic has a considerable advantage over the original statistic.As an example,the variance change of Shanghai Composite Index is given.