A Primer on Statistical Analysis of Dynamical Systems in Historical Social Sciences (with a Particular Emphasis on Secular Cycles)

Peter Turchin
Structure and Dynamics January 2, 2005 Journal Link PDF


This primer explicates the conceptual foundations of the statistical approach to detecting dynamical feedbacks. It is assumed that we have time-series data on several aspects of the studied system. The basic idea of the approach is to regress discrete rates of change of measured variables on variables themselves. I discuss several issues involved in the analysis, such as how to select the appropriate time step, or the delay parameter. The goal of the analysis is to determine whether a particular predictor variable, or set of variables, has a statistically detectable effect on the response. This is accomplished by cross-validation.
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