Single Case Studies: The Time Series vs. the Smoothing Regression Approach
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Single case studies are usually evaluated by time series intervention analysis, a well developed parametric approach. This paper discusses the most advanced technique, theoretically speaking, of Box and Tiao (1975), pointing out conceptual problems and limitations. As an alternative, a new non-parametric approach is introduced for trend estimation, an approach which makes it possible to accommodate linear stochastic noise processes from the Box and Jenkins (1976) methodology. It is called Dependent Error Regression Smoothing (DERS; Schimek, 1992, 1994). Conceptual differences from parametric time series intervention analysis are explored. An example is cited from clinical psychology in which parametric approaches fail to provide any evidence for an intervention effect on an observational series. The example data set is re analysed in the non-parametric framework of DERS, and the intervention effect under consideration can then be identified.
KeywordsAR ARMA intervention analysis intervention function MA non-parametric regression penalized least squares prefiltering pseudo-variance single case study smoothing parameter smoothing spline time series trend estimation
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