We examine the use of the random walk hypothesis on the BRICS stock indices. Our examination of the stock indices uses a recently developed wavelet-based unit root test by Fan and Gençay (2010) along with a battery of unit root tests. We also examine the sensitivity of the wavelet-based unit root test. Our wavelet-based unit root tests show evidence that rejects the null of the unit root for all of the BRICS countries except for the Russian Federation. Hence, the tests provide support for the predictability of stock market indices in these economies on the basis of historical information. However, there is a need for caution because the results are based on a relatively small sample of only 11years of monthly observations.