This study undertakes the challenging task of comparing the weak form efficiency of conventional and Islamic equity markets. Using 12 different Dow Jones indexes that cover 16 years of daily data, we compare the time-varying non-linear predictability patterns of conventional market indexes and their Islamic counterparts at country and continent level by using permutation entropy. Accordingly, we find that all indexes in our analysis have different degrees of time-varying predictability and all conventional markets are found to be more efficient compared to their Islamic counterparts. However, in some of the cases, this difference in efficiency is almost indistinguishable. Our findings reveal that compared to their conventional counterparts, Islamic markets do not necessarily need to carry a more deterministic or predictable structure since efficiency in these markets depends mostly on liquidity, market quality, institutional characteristics and the country/continent specific investment behavior. (C) 2014 Elsevier Inc. All rights reserved.