Introduction and Basic Theoretical Concepts

Time series analysis is an integral part of every empirical investigation which aims at describing and modeling the evolution over time of a variable or a set of variables in a statistically coherent way. The economics of time series analysis is thus very much intermingled with macroeconomics and finance which are concerned with the construction of dynamic models. In principle, one can approach the subject from two complementary perspectives. The first one focuses on descriptive statistics. It characterizes the empirical properties and regularities using basic statistical concepts like mean, variance, and covariance. These properties can be directly measured and estimated from the data using standard statistical tools. Thus, they summarize the external (observable) or outside characteristics of the time series. The second perspective tries to capture the internal data generating mechanism. This mechanism is usually unknown in economics as the models developed in economic theory are mostly of a qualitative nature and are usually not specific enough to single out a particular mechanism. Thus, one has to consider some larger class of models. By far most widely used is the class of autoregressive moving-average (ARMA) models which rely on linear stochastic difference equations with constant coefficients. Of course, one wants to know how the two perspectives are related which leads to the important problem of identifying a model from the data.