Testing the random walk hypothesis through robust estimation of correlation

This paper uses Monte Carlo simulations to examine the properties of the conventional Pearson and some of the most well-known robust to outliers estimators of correlation in the presence of general heteroskedasticity. We show that the tests of a random walk based on the Pearson autocorrelation coefficient, including the Lo and MacKinlay [1988. Stock market prices do not follow random walks: evidence from a simple specification test. Rev. Financial Studies 1, 41–66] robust form of the variance-ratio test, can be unreliable in the presence of some forms of conditional heteroskedasticity. As an alternative to the Pearson autocorrelation coefficient, we propose the median coefficient of autocorrelation. Our simulation results show that, in contrast to the Pearson autocorrelation coefficient, the median coefficient of autocorrelation is robust to conditional heteroskedasticity. When applied to exchange rate returns, the variance-ratio test based on the median autocorrelation coefficient provides stronger evidence against the random walk hypothesis compared with the Lo and MacKinlay [1988. Stock market prices do not follow random walks: evidence from a simple specification test. Rev. Financial Studies 1, 41–66] robust variance-ratio test.