  We introduce a general method for the study of memory in symbolic sequences
based on higher-order Markov analysis. The Markov process that best represents
a sequence is expressed as a mixture of matrices of minimal orders, enabling
the definition of the so-called memory profile, which unambiguously reflects
the true order of correlations. The method is validated by recovering the
memory profiles of tunable synthetic sequences. Finally, we scan real data and
showcase with practical examples how our protocol can be used to extract
relevant stochastic properties of symbolic sequences.
