Monitoring shifts in mean: Asymptotic normality of stopping times

被引：17

作者：

Aue, Alexander ^{[4
]}

Horvath, Lajos ^{[2
]}

Kokoszka, Piotr ^{[1
]}

Steinebach, Josef ^{[3
]}

机构：

[1] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[3] Univ Cologne, Inst Math, D-5000 Cologne, Germany

[4] Clemson Univ, Dept Math Sci, Clemson, SC USA

来源：

TEST | 2008年 / 17卷 / 03期

基金：

美国国家科学基金会;

关键词：

Asymptotic normality; Change in the mean; CUSUM; Sequential detection;

D O I：

10.1007/s11749-006-0041-7

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a sequential procedure designed to detect a possible change in the mean of a random sequence. The procedure is motivated by the problem of detecting an early change in the mean of returns and is based on the CUSUM (cumulative sum) statistic. It terminates when the CUSUM crosses a boundary function or the number of collected observations reaches a prescribed number. We show that the stopping time is asymptotically normal. Simulations using models derived from returns on indexes and individual stocks show that the normal approximation holds in finite samples.

引用

页码：515 / 530

页数：16

共 21 条

[1] AN IMPROVED HETEROSKEDASTICITY AND AUTOCORRELATION CONSISTENT COVARIANCE-MATRIX ESTIMATOR [J].