Asymptotic inference for unit root processes with GARCH(1,1) errors

被引：44

作者：

Ling, SQ ^{[1
]}

Li, WK

机构：

[1] Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China

[2] Hong Kong Univ Sci & Technol, Hong Kong, Hong Kong, Peoples R China

来源：

ECONOMETRIC THEORY | 2003年 / 19卷 / 04期

关键词：

D O I：

10.1017/S0266466603194029

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

This paper investigates the so-called one-step local quasi-maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling and Li (1998, Annals of Statistics 26, 84-125) and can be used to construct the unit root test.

引用

页码：541 / 564

页数：24

共 20 条

[1]

Billingsley P, 1968, CONVERGE PROBAB MEAS

[2] GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY [J].

BOLLERSLEV, T .

JOURNAL OF ECONOMETRICS, 1986, 31 (03) :307-327

[3]

Bollerslev T, 1994, Handbook of econometrics, V4, P2959, DOI [10.1016/S1573-4412(05)80018-2, DOI 10.1016/S1573-4412(05)80018-2]

[4] LIMITING DISTRIBUTIONS OF LEAST-SQUARES ESTIMATES OF UNSTABLE AUTOREGRESSIVE PROCESSES [J].

CHAN, NH ;

WEI, CZ .

ANNALS OF STATISTICS, 1988, 16 (01) :367-401

[5]

DAVIS RA, 1999, SAMPLE ACF MULTIVARI

[6]

HALL P, 1980, MARTINGALE LIMIT THE

[7] Asymptotic theory of LAD estimation in a unit root process with finite variance errors [J].

Herce, MA .

ECONOMETRIC THEORY, 1996, 12 (01) :129-153

[8] WEAK LIMIT-THEOREMS FOR STOCHASTIC INTEGRALS AND STOCHASTIC DIFFERENTIAL-EQUATIONS [J].

KURTZ, TG ;

PROTTER, P .

ANNALS OF PROBABILITY, 1991, 19 (03) :1035-1070

[9] ASYMPTOTIC THEORY FOR THE GARCH(1,1) QUASI-MAXIMUM LIKELIHOOD ESTIMATOR [J].

LEE, SW ;

HANSEN, BE .

ECONOMETRIC THEORY, 1994, 10 (01) :29-52

[10]

Ling SQ, 1998, ANN STAT, V26, P84

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