# CHAPTER 14

# REGRESSION ANALYSIS OF TIME SERIES DATA

## 14.1 INTRODUCTION TO REGRESSION MODELS FOR TIME SERIES DATA

Many applications of regression involve both predictor and response variables that are **time series**, that is, the variables are time-oriented. Regression models using time series data occur relatively often in economics, business, and many fields of engineering. The assumption of uncorrelated or independent errors that is typically made for regression data that is not time-dependent is usually not appropriate for time series data. Usually the errors in time series data exhibit some type of **autocorrelated** structure. By autocorrelation we mean that the errors are correlated with themselves at different time periods. We will give a formal definition shortly.

There are several **sources** of autocorrelation in time series regression data. In many cases, the cause of autocorrelation is the failure of the analyst to include one or more important predictor variables in the model. For example, suppose that we wish to regress the annual sales of a product in a particular region of the country against the annual advertising expenditures for that product. Now the growth in the population in that region over the period of time used in the study will also influence the product sales. Failure to include the population size may cause the errors in the model to be positively autocorrelated, because if the per-capita demand for the product is either constant or increasing with time, population ...