We present a direct way to model short- and medium-range correlations in DNA sequences and to separate them from long-range correlations. To do so, we discuss symbol sequences generated by a discrete autoregressive process of order p, DAR(p). These sequences display higher-order Markov...

We investigate the probability of observing a given pattern of n rises and falls in a random stationary data series. The data are modeled as a sequence of n+1 independent and identically distributed random numbers. This probabilistic approach has a combinatorial equivalent, where the data are...