A discrete autoregressive process as a model for short-range correlations in DNA sequences

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 properties but are based on very few parameters. The aim of our investigation is (1) to introduce with such DAR(p) processes a parameter-efficient tool for generating higher-order Markov processes on a discrete alphabet, (2) to study, how the parameters of the process determine the statistical properties of the sequence and (3) to provide the mathematical tools for estimating the parameters from a given experimental sequence. The statistical properties of the generated sequences, expressed in terms of parameters in the DAR(p) process, are monitored with methods from information theory. The implications of our findings for DNA sequences are discussed and some application is given. In particular, it is shown, how short-range correlations in DNA sequences can be parameterised by such a process.