CONSISTENCY AND LIMITING DISTRIBUTION OF THE LEAST-SQUARES ESTIMATOR OF A THRESHOLD AUTOREGRESSIVE MODEL

被引：805

作者：

CHAN, KS

机构：

来源：

ANNALS OF STATISTICS | 1993年 / 21卷 / 01期

关键词：

COMPOUND POISSON PROCESS; CONSISTENCY; ERGODICITY; LEAST SQUARES ESTIMATION; LIMITING DISTRIBUTION; THRESHOLD AUTOREGRESSIVE MODELS;

D O I：

10.1214/aos/1176349040

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：

It is shown that, under some regularity conditions, the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent. The limiting distribution of the least squares estimator is derived. It is shown that the estimator of the threshold parameter is N consistent and its limiting distribution is related to a compound Poisson process.

引用

页码：520 / 533

页数：14

共 13 条

[1] A MULTIPLE-THRESHOLD AR(1) MODEL [J].

CHAN, KS ;

PETRUCCELLI, JD ;

TONG, H ;

WOOLFORD, SW .

JOURNAL OF APPLIED PROBABILITY, 1985, 22 (02) :267-279

[2] ON THE USE OF THE DETERMINISTIC LYAPUNOV FUNCTION FOR THE ERGODICITY OF STOCHASTIC DIFFERENCE-EQUATIONS [J].

CHAN, KS ;

TONG, H .

ADVANCES IN APPLIED PROBABILITY, 1985, 17 (03) :666-678

[3]

CHAN KS, 1988, 245 U CHIC DEP STAT

[4]

HUBER PJ, 1967, 5TH P BERK S MATH ST, V1, P221

[5]

IBRAGIMOV IA, 1981, STATISTICAL ESTIMATI

[6]

KUSHNER H., 1984, APPROXIMATION WEAK C

[7]

NEVEU J, 1965, MATH F CALCULUS PROB

[8] A THRESHOLD AR(1) MODEL [J].

PETRUCCELLI, JD ;

WOOLFORD, SW .

JOURNAL OF APPLIED PROBABILITY, 1984, 21 (02) :270-286

[9]

Petruccelli Joseph D., 1986, J TIME SER ANAL, V7, P269, DOI [10.1111/j.1467-9892.1986.tb00494.x, DOI 10.1111/J.1467-9892.1986.TB00494.X]

[10]

TONG H, 1986, LECTURE NOTES STATIS, V21

← 1 2 →