This paper aims at understanding the statistical features of nucleic acid sequences from the knowledge of the dynamical process that produces them. Two studies are carried out: first, mutual information function of the limiting sequences generated by simple sequence manipulation dynamics with replications and mutations are calculated numerically (sometimes analytically). It is shown that elongation and replication can easily produce long-range correlations. These long range correlations could be destroyed in various degrees by mutation in different sequence manipulation models. Second, mutual information functions for several human nucleic acids sequences are determined. It is observed that intron sequences (noncoding sequences) tend to have longer correlation lengths than exon sequences (protein-coding sequences).