Spectral analysis for categorical time series: Scaling and the spectral envelope

Many studies produce categorical time series in which harmonic analysis is of interest. Although there exist time domain approaches for the analysis of categorical time series such as Markov chains or link function based regression models, there is apparently little statistical theory or methodology for analyzing qualitative-valued time series in the frequency domain. The purpose of this paper is to initiate the development of a general framework for the frequency domain analysis of categorical time series. In doing so, we discuss the scaling of categorical time series and introduce a new concept that we call the spectral envelope of a categorical time series. We demonstrate our methodology on a data set from a problem in molecular biology.