Serial Dependency in Single-Case Time Series
Thomas A. Matyas and Kenneth M. Greenwood La Trobe University
The idea that behavior is not random is fundamental to the concept of psychological and behavioral sciences. Behavior emanates from an individual organism and inevitably forms a chronological sequence. Thus, psychological science needs to establish, inter alia, models of the patterns of behavior as ordered in time. The same may be said of the underlying psychological and physico-chemical substrates that have been presumed to be involved in the causation of this behavior. In the ideal of science these models are thought to be valuable both as representations of knowledge about the causal phenomena and as tools for building an applied science, a technology of prediction and evaluation. Indeed, this technological goal is exemplified in this book, wherein time- series designs are discussed as a tool for investigation and management of individual cases.
The purpose of this chapter, therefore, is to review the issue of predictability across time in behavioral time series. To achieve this aim, the chapter considers the definition of serial dependence and examines how it can arise out of a variety of patterns over time. This is a necessary prelude to an informed and detailed discussion of both why serial dependence matters and whether it is present in behavioral time series. The chapter shows how the presence and nature of serial dependence is not only an issue in our conceptualization of behavior, but also a practical problem in the analysis of single-case data. Serial dependence patterns reflect the mathematical structure and graphic shape of the time series. Not surprisingly, therefore, it has been shown to affect the statistical analysis of single-case data. In addition, serially dependent data