ABSTRACT
In basic statistical analysis, attention is usually focused on data samples, X1, X2, … , Xn, where the Xis are independent and identically distributed random variables. In a typical introductory course in univariate mathematical statistics, the case in which samples are not independent but are in fact correlated is not generally covered. However, when data are sampled at neighboring points in time, it is very likely that such observations will be correlated. Such time-dependent sampling schemes are very common. Examples include the following:
• Daily Dow Jones stock market closes over a given period • Monthly unemployment data for the United States • Annual global temperature data for the past 100 years • Monthly incidence rate of influenza • Average number of sunspots observed each year since 1749 • West Texas monthly intermediate crude oil prices • Average monthly temperatures for Pennsylvania
Note that in each of these cases, an observed data value is (probably) not independent of nearby observations. That is, the data are correlated and are therefore not appropriately analyzed using univariate statistical methods based on independence. Nevertheless, these types of data are abundant in fields such as economics, biology, medicine, and the physical and engineering sciences, where there is interest in understanding the mechanisms underlying these data, producing forecasts of future behavior, and drawing conclusions from the data. Time series analysis is the study of these types of data, and in this book we will introduce you to the extensive collection of tools and models for using the inherent correlation structure in such data sets to assist in their analysis and interpretation.
