![]() Time series analysis has three goals: forecasting, modelling, and characterization. In both cases, the goal is to explain observations we will not consider the important related problem of using knowledge about a system for controlling it in order to produce some desired behaviour. Understanding is based on explicit mathematical insight into how systems behave, and learning is based on algorithms that can emulate the structure in a time series. We will use the terms understanding” and learning” to refer to two complementary approaches taken to analyze an unfamiliar time series. For example, the motion of a pendulum or the rhythm of the seasons carries within them the potential for predicting their future behaviour from knowledge of their oscillations without requiring insight into the underlying mechanism. In this chapter we will focus on phenomena for which underlying equations are not given the rules that govern the evolution must be inferred from regularities in the past. To make a forecast if the equations are not known, one must find both the rules governing system evolution and the actual state of the system. ![]()
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