Testing for long memory in the presence of a general trend

被引:55
作者
Giraitis, L
Kokoszka, P
Leipus, R
机构
[1] London Sch Econ, Dept Econ, London WC2A 2AE, England
[2] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England
[3] Vilnius Univ, Dept Math & Informat, LT-2600 Vilnius, Lithuania
关键词
long memory; trend; change point;
D O I
10.1017/S0021900200019215
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
The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharya et al. (1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo's (1991) modified R/S test. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool the R/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger than N-1/2, where N is the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.
引用
收藏
页码:1033 / 1054
页数:22
相关论文
共 36 条
[1]  
Anderson T. W., 1971, STAT ANAL TIME SERIE
[2]  
BAUM CF, 1999, J INT FINANC MARK I, V9, P359
[3]   THE HURST EFFECT UNDER TRENDS [J].
BHATTACHARYA, RN ;
GUPTA, VK ;
WAYMIRE, E .
JOURNAL OF APPLIED PROBABILITY, 1983, 20 (03) :649-662
[4]  
BILLINGSLEY P., 1999, Convergence of Probability Measures, V2nd, DOI 10.1002/9780470316962
[5]  
Bos C.S., 1999, Empir. Econ., V24, P427
[6]  
BUHLMANN P, 1996, J TIME SER ANAL, V17, P123
[7]  
Campbell J., 1997, The econometrics of financial markets
[8]   INVARIANCE PRINCIPLE FOR STATIONARY PROCESSES [J].
DAVYDOV, YA .
THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1970, 15 (03) :487-&
[9]   Long memory and regime switching [J].
Diebold, FX ;
Inoue, A .
JOURNAL OF ECONOMETRICS, 2001, 105 (01) :131-159
[10]   Stationary ARCH models: Dependence structure and central limit theorem [J].
Giraitis, L ;
Kokoszka, P ;
Leipus, R .
ECONOMETRIC THEORY, 2000, 16 (01) :3-22