A novel approach is presented to the detection of homological, eroded and latent periodicities in DNA sequences. Each symbol in a DNA sequence is assumed to be generated from an information source with an underlying probability mass function (pmf) in a cyclic manner. The number of sources can be interpreted as the periodicity of the sequence. The maximum likelihood estimates are developed for the pmfs of the information sources as well as the period of the DNA sequence. The statistical model can also be utilized for building probabilistic representations of RNA families.