A strong convergence rate of estimator of variance change in linear processes and its applications. Issue 2 (4th March 2017) - Qin, Ruibing; Liu, Weiqi; Tian, Zheng
ABSTRACT: Let{ Y n, n ≥ 1 } be a linear process such thatY i = μ + σ 1 e i, i ≤ k 0 andY i = μ + σ 2 e i, i ≥ k 0 + 1, wherek 0 is a change point, μ, σ 1 andσ 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 rateo ( M ( n ) / n ), whereM ( 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.