We investigate financial market efficiency in the time series of four daily Baltic stock market indices, namely: Baltic Benchmark Gross Index (OMXBBGI), all share index of Tallin-Lithuanian (OMXT), all share index of Riga (OMXR) and all share index of Vilnius (OMXV), based on historical data from 1 January, 2000 to 22 January 2016. We use fractional integration methods to test the hypothesis of market efficiency. Realizing that long-memory estimation could be spurious in the presence of structural breaks, we identify bull and bear market phases from each of the time series. Applying the fractional integration approach, we find that the random walk hypothesis of market efficiency is generally rejected in the overall, and at two bull and one bear sub-samples of the four Baltic stock indices. The volatility at the bear markets of these stocks persists more than the volatility at the bull markets. Our results therefore provide evidence for weak form of market efficiency in the Baltic stock markets, with some exceptions. As a way of policy, the results are relevant to portfolio managers and policy makers in a number of ways. (C) 2018 Elsevier B.V. All rights reserved.