Time Series and Stochastic Processes

This chapter addresses some statistical modeling approaches for time series data and discusses their potential for psychometric applications. We adopt a broad conceptualization of time series, including under this rubric any type of data that involves serial statistical dependence. Such dependence may be represented in continuous time, discrete time, or in a purely sequential manner. This chapter begins by discussing the relationships among these three representations and offers some general advice on when each might prove useful. We then provide an overview of three modeling frameworks that exemplify the different representations of statistical dependence: Markov decision processes, state-space modeling, and temporal point processes. For each modeling framework, we discuss its specification, its psychometric interpretation, and provide a brief numeric example including R code.