A strong convergence rate of estimator of variance change in linear processes and its applications

Let {Yn, n >= 1} be a linear process such that Y-i = mu + sigma(1)e(i), i <= k(0) and Y-i = mu + sigma(2)e(i), i >= k(0) + 1, where k(0) is a change point, mu, sigma(1) and sigma(2) are unknown parameters and {e(i), i >= 1} is an infinite-order moving average process which satisfies some assumptions. In this paper we investigate the strong convergence rate of the estimator of the variance change and derive a strong convergence rate o(M(n)/n), where M(n) is a natural number sequence and increase to infinity as the sample size n increase to infinity. On the basis of the results, we apply an iterative algorithm to search for the variance change more effectively. A simple simulation study demonstrates that the algorithm is efficient. Additionally, an empirical application is given for illustration.