Comparing Different Permutation Tests with Dickey-Fuller Tests for Unit Root in the Autoregressive Time Series

Three permutation tests based Tn (Li et al. (2013)), KSn and BKRn (Blum et al.(1961)) for unit root in the AR(1) time series are investigated and compared to Dickey-Fuller tests with white noise from distributions at different levels of skewness (symmetric distributions such as standard normal; slightly skewed distributions such as Chisq (1); highly right skewed distributions such as Weibull (shape=1/3, scale=1); highly left skewed distributions such as negative lognormal (µ = 0, s = 2)) and two moderately skewed F distributions with numerator degree of freedom 1 and denominator degrees of freedom 7 and 4. As expected, Dickey-Fuller tests overperform the permutation tests when white noise is from symmetric distributions or slightly skewed distributions. The permutation tests based on BKRn perform at least comparable to and most of the time overperform the permutation tests based on KSn regardless of the levels of skewness of white noise distributions. The permutation tests based on Tn could not compare to Dickey-Fuller tests when white noise is from symmetric distributions and it could not compare to the permutation tests based on BKRn when white noise is from skewed distributions. JEL classification numbers: C12, C14, C15. Keywords: Permutation tests, Autoregressive, Unit root.