A strong convergence rate of estimator of variance change in linear processes and its applications. Issue 2 (4th March 2017)

• Record Type: Journal Article
• Authors: Qin, Ruibing; Liu, Weiqi; Tian, Zheng
• Is Part Of: Statistics. Volume 51:Issue 2(2017)
• Page Start: 314
• Page End: 330
• Publication Date: 2017-03-04
• Subjects: Variance change -- linear processes -- the CUSUM estimator -- strong convergence; 62F03 -- 62F05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2016.1268614
• Languages: English
• ISSNs: 0233-1888

Abstract

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.