Time Series Analysis

In some applications, researchers collect longitudinal data for one or more subjects over a (usually) extended period of time. In the field of economics, for example, the federal government of the United States measures the nation’s gross domestic product every month, creating a long longitudinal record of gross domestic product over time. Similarly, meteorologists record measurements on temperature and rainfall, monitoring every day at stations around the world. Again, the resulting data set contains a great many measurements taken over a long period of time for each of these stations. Psychologists [Page 1702]may collect such time series data in the form of diary entries in which participants are asked to record the number of times that they have certain thoughts or engage in specific behaviors over the course of each day, over many weeks or months. Educational researchers might look at student assessment scores across many years. The resulting observations represent a time series data set.

In all of these examples, the common trait is the recording of data values longitudinally for an extended period of time. The statistical methodologies designed to deal with these longitudinal records are known collectively as time series analysis. Time series analysis differs from more traditional repeated measures data in that the number of data points is much larger in the former than the latter, which typically involves only a few measurements for each individual. However, some of the same issues that are created by the collection of repeated measures data are also present in time series. For example, one of the core assumptions underlying many statistical analyses is the independence of the specific data points used. However, a signal quality of time series data is the presence of correlation in measurements taken over time (referred to as autocorrelation). In other words, a measurement made at time t is likely to be correlated with a measurement made at the immediately preceding time, t − 1. Indeed, it is entirely possible that the measurement at time t is autocorrelated with measurements at t − 2, t − 3, and so on, although the magnitude of this relationship would be expected to decline over time.

Given this lack of independence in data points, standard analyses such as regression are not appropriate to use with time series data because this serial correlation structure leads to biased estimation, particularly for model parameter standard errors. This fact has given rise to an entire family of procedures designed to correctly model the autocorrelation that is present in time series, and indeed to use it for forecasting future measurements, as well as correct other modeling procedures such as regression. In the following paragraphs, discuss some of the basic time series models that are available for researchers and data analysts to use are discussed. However, it should be noted that these represent only a small number of all of the possible models that can be used with time series data.