Analysis of Time Series

The study of time series is an essential aspect of Intelligent Data Analysis. The field is very broad, and it has been treated with very different methodological approaches, ranging from differential equations to stochastic models and to AI-based systems. The lesson will present time series analysis as a part of the general problem of modelling dynamical systems. The framework of systems’ theory will provide a general view of such problem, and it will permit to coherently overview the majority of the time series analysis approaches. In more detail, the principles of systems theory will be first discussed; the concept of “dynamical system” will be investigated and some results of systems theory will be presented. The notions of state, equilibrium, linearity, observability and reachability will be discussed. Some modelling tools will be then introduced, ranging from black-box to structural models. Stochastic linear and non linear models will be briefly described, including AR, MA, and ARMAX models. Moreover, a method to obtain structural information from input/output data will be introduced. The lesson will finally show how the knowledge on systems dynamics can be effectively exploited in the time series clustering problem. Distance-based, model-based and template-based will be revisited in order to account for information on the systems dynamics.