  This article introduces a novel approach to the classification of categorical
time series under the supervised learning paradigm. To construct meaningful
features for categorical time series classification, we consider two relevant
quantities: the spectral envelope and its corresponding set of optimal
scalings. These quantities characterize oscillatory patterns in a categorical
time series as the largest possible power at each frequency, or spectral
envelope, obtained by assigning numerical values, or scalings, to categories
that optimally emphasize oscillations at each frequency. Our procedure combines
these two quantities to produce an interpretable and parsimonious feature-based
classifier that can be used to accurately determine group membership for
categorical time series. Classification consistency of the proposed method is
investigated, and simulation studies are used to demonstrate accuracy in
classifying categorical time series with various underlying group structures.
Finally, we use the proposed method to explore key differences in oscillatory
patterns of sleep stage time series for patients with different sleep disorders
and accurately classify patients accordingly.
