Principles of Time Series Analysis

In this study of nonlinear dynamical systems (NDS), as with any other approach to building statistical models, we have to be mindful of three sorts of questions. What are the events in the physical world and in our mental covariates of that world we seek to model? What can we choose as representational structures in symbols, algebra, or logical relations that are intrinsically tractable? And what rules can we adopt for evaluating the relative worth of alternative models of the real world? It is possible to build general theories about finding a hierarchical order for alternative models, but these are incomplete (Speekenbrink, 2003). These three areas of discourse, data, models, and mapping between data and models, all involve decisions about what is thought to be scientifically relevant and potentially fruitful to predict in a wider range of apparently related scenarios.