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In this study, it is examined how to use long-term memory models for predicting the dynamics of cryptocurrencies. In this framework, all the most suitable models provide an adequate error at the level of a 5% confidence interval. The authors believe that the IGARCH and GJRGARCH models provide the best results in terms of modeling the volatility of the most popular cryptocurrencies. The IGARCH model is similar to the standard GARCH model with the addition of only the conditional volatility process with infinite memory. Due to the growing demand and interest in cryptocurrencies and crypto assets in general, the authors believe that they should be considered as a new segment of the financial market. There are many more questions about whether cryptocurrencies should be classified as currencies or as a commodity. Our analysis suggests that cryptocurrencies are financial assets. Most operations with them are carried out for investment purposes: either as long-term investments in new technologies, or in order to obtain short-term profits.