This paper tests the finite sample properties of the Kuan and Lee's (KL) test to study market efficiency by mean of extensive Monte Carlo experiments using different data generating processes. We apply the KL test with and without wild bootstrap on the six global stock indices covering major US, European and Asian stock markets to test the martingale difference hypothesis. In addition, we apply a moving sub-sample approach to examine the evolution of market efficiency over time and to obtain inferential findings that are robust to the presence of influential outliers. We find a significant improvement in the small sample properties of the KL test under conditional heteroskedasticity when applied with the wild bootstrap procedure. On the empirical side, we find that, except for the German stock market, all the other markets under study have become more efficient after the sub-prime crisis.