Categorical time series analysis and applications in statistical quality control

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Categorical (nominal) time series are prevalent across various fields such as computer science, biology, and linguistics. Despite their significance, there is a lack of comprehensive literature addressing categorical time series analysis, with existing research scattered across diverse scientific journals. Standard statistical tools often fail to apply, as there is no established repertoire of distributions, and visual analysis poses challenges. Techniques used in cardinal time series analysis, such as seasonal adjustment or trend elimination, are not applicable, and defining 'trend' or 'season' for categorical data is complex. This text aims to thoroughly explore categorical time series analysis in the time domain, integrating known and new findings into a cohesive framework. Chapter I focuses on exploratory analysis, reviewing methods for sequence comparison and pattern detection. Chapter II introduces fundamental concepts, proposing weak stationarity forms relevant for modeling and defining serial dependence measures. Chapter III discusses various models for categorical processes, including Bernoulli and Markov types, with a detailed examination of binary processes. Chapter IV investigates statistical analysis approaches, exploring patterns and models for time series of counts derived from categorical processes. Chapter V applies insights from previous chapters to design monitoring and control strategies for categorical p