  The growing attention on cryptocurrencies has led to increasing research on
digital stock markets. Approaches and tools usually applied to characterize
standard stocks have been applied to the digital ones. Among these tools is the
identification of processes of market fluctuations. Being interesting
stochastic processes, the usual statistical methods are appropriate tools for
their reconstruction. There, besides chance, the description of a behavioural
component shall be present whenever a deterministic pattern is ever found.
Markov approaches are at the leading edge of this endeavour. In this paper,
Markov chains of orders one to eight are considered as a way to forecast the
dynamics of three major cryptocurrencies. It is accomplished using an empirical
basis of intra-day returns. Besides forecasting, we investigate the existence
of eventual long-memory components in each of those stochastic processes.
Results show that predictions obtained from using the empirical probabilities
are better than random choices.
