The asymptotic distribution of CUSUM estimator based on α-mixing sequences

被引：4

作者：

Gao, Min ^{[1
]}

Ding, Saisai ^{[1
]}

Wu, Shipeng ^{[1
]}

Yang, Wenzhi ^{[1
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei, Peoples R China

来源：

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION | 2022年 / 51卷 / 10期

关键词：

Brownian bridge; Change point detection; CUSUM estimator; alpha-mixing sequence; CENTRAL LIMIT-THEOREM; CHANGE-POINT; STRUCTURAL-CHANGES; SQUARES; INEQUALITIES; CONVERGENCE;

D O I：

10.1080/03610918.2020.1794006

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：

In this paper, we consider the CUSUM estimator based on alpha-mixing sequences. By giving the consistency estimators for mean and covariance functions, the limit distribution of CUSUM estimator is presented as a standard Brownian bridge, which can be used in the change point detection. As applications, some simulations and real data examples are illustrated to test our CUSUM estimator.

引用

页码：6101 / 6113

页数：13

共 27 条

[1] The CUSUM Test for Detecting Structural Changes in Strong Mixing Processes [J].

Azizzadeh, F. ;

Rezakhah, S. .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2014, 43 (17) :3733-3750

[2]

Bai J., 1994, J TIME SER ANAL, V15, P453, DOI [10.1111/j.1467-9892.1994.tb00204.x, DOI 10.1111/J.1467-9892.1994.TB00204.X]

[3] DETECTING LEVEL SHIFTS IN TIME-SERIES [J].

BALKE, NS .

JOURNAL OF BUSINESS & ECONOMIC STATISTICS, 1993, 11 (01) :81-92

[4]

Billingsley Patrick., 2013, CONVERGE PROBAB MEAS

[5] PROBLEM OF NILE - CONDITIONAL SOLUTION TO A CHANGEPOINT PROBLEM [J].

COBB, GW .

BIOMETRIKA, 1978, 65 (02) :243-251

[6] CONVERGENCE OF DISTRIBUTIONS GENERATED BY STATIONARY STOCHASTIC PROCESSES [J].

DAVYDOV, YA .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1968, 13 (04) :691-&

[7] THE ASYMPTOTIC-BEHAVIOR OF SOME NONPARAMETRIC CHANGE-POINT ESTIMATORS [J].

DUMBGEN, L .

ANNALS OF STATISTICS, 1991, 19 (03) :1471-1495

[8] Variance Targeting Estimation of Multivariate GARCH Models [J].

Francq, Christian ;

Horvath, Lajos ;

Zakoian, Jean-Michel .

JOURNAL OF FINANCIAL ECONOMETRICS, 2016, 14 (02) :353-382

[9]

Hall P., 1980, MARTINGALE LIMIT THE

[10] A FUNCTIONAL CENTRAL LIMIT-THEOREM FOR STRONGLY MIXING SEQUENCES OF RANDOM-VARIABLES [J].

HERRNDORF, N .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1985, 69 (04) :541-550

← 1 2 3 →