Some Inference About Change In Variance

In this paper, we have studied the situation that there is only change point in variance in independent random variable sequences and the situation that there are both change point in mean and variance in independent random variable sequences with sliding window method, we have given the test statistics and the estimator of the change point, and the asymptotic distribution of the test statistics, we have also proved the weak convergence speed and strong convergence speed of the estimator of change point. We have studied the situation that the variance of the fluctuation of AR(1) model exist a change point and the situation that the variance of the fluctuation and the autoregressive coefficient of AR(1) model both exist a change point with maximum likelihood ratio method, we have given the asymptotic distribution of the test statistics and the estimator of the change point. We have made a simulation of the change point in AR(1) model, to analysis the goodness of the test statistics in different sample sizes and change point position.