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This paper tests the random walk hypothesis in the cryptocurrency market. Based on the well-known Meese–Rogoff puzzle, we evaluate whether cryptocurrency returns are predictable or not. For this purpose, we conduct in-sample and out-of-sample analyses to examine the forecasting power of our model built with autoregressive components and lagged returns of BITCOIN, compared with the random walk benchmark. To this end, we considered the 13 major cryptocurrencies between 2018 and 2022. Our results indicate that our models significantly outperform the random walk benchmark. In particular, cryptocurrencies tend to be far more persistent than regular exchange rates, and BITCOIN (BTC) seems to improve the predictive accuracy of our models for some cryptocurrencies. Furthermore, while the predictive performance is time varying, we find predictive ability in different regimes before and during the pandemic crisis. We think that these results are helpful to policymakers and investors because they open a new perspective on cryptocurrency investing strategies and regulations to improve financial stability. [ABSTRACT FROM AUTHOR]