Premium
A small‐sample overlapping variance‐ratio test
Author(s) -
Tse Y. K.,
Ng K. W.,
Zhang Xibin
Publication year - 2004
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1046/j.0143-9782.2003.01804.x
Subject(s) - mathematics , statistics , test statistic , null distribution , sample size determination , statistic , monte carlo method , asymptotic distribution , z test , null hypothesis
. The null distribution of the overlapping variance‐ratio (OVR) test of the random‐walk hypothesis is known to be downward biased and skewed to the right in small samples. As shown by Lo and MacKinlay (1989), the test under‐rejects the null on the left tail seriously when the sample size is small. This property adversely affects the applicability of the OVR test to macroeconomic time series, which usually have rather small samples. In this paper, we propose a modified overlapping variance‐ratio statistic and derive its exact mean under the normality assumption. We propose to approximate the small‐sample distribution of the modified statistic using a beta distribution that matches the (exact) mean and the (asymptotic) variance. A Monte Carlo experiment shows that the beta approximation performs well in small samples.