Localizing time-varying periodicities in symbolic sequences

A novel approach is presented for the detection and localization of changing periodicities in symbolic sequences. Various symbolic sequences like DNA can be modelled as stochastic processes that exhibit time-varying cyclostation- arity. The coding regions of the DNA, for instance, exhibit statistical periodicity with period three. The complexity-regularized maximum-likelihood estimates are developed in this paper for the statistical period of symbolic sequences. The changing periodicities along the sequence are discovered by using sliding windows. A cumulative sum test is also presented to detect the change points. The formulation in this paper avoids any kind of numerical mapping for the symbolic DNA sequences and does not impose any algebraic structure.