Characteristics of Time Series

Abstract

Statistical inference is about learning something that is unknown from the known. Time series analysis is no exception in this aspect. In order to achieve this, it is necessary to assume that at least some features of the underlying probability law are sustained over a time period of interest. This leads to the assumptions of different types of stationarity, depending on the nature of the problem at hand. The dependence in the data marks the fundamental difference between time series analysis and classical statistical analysis. Different measures are employed to describe the dependence at different levels to suit various practical needs. In this chapter, we introduce the most commonly used definitions for stationarity and dependence measures. We also make comments on when those definitions and measures are most relevant in practice.