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 , 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.
Beta distribution, Monte Carlo experiment, random-walk hypothesis, variance-ratio test
Journal of Time Series Analysis
TSE, Yiu Kuen; NG, K. W.; and ZHANG, Xibin.
A Small-Sample Overlapping Variance-Ratio Test. (2004). Journal of Time Series Analysis. 25, (1), 127-135. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/149
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