In Chapters 4 and 5 we discussed estimation methods for β under departures from the exogeneity and homoscedasticity assumptions. This chapter extends the discussion to the case when the assumption of independent disturbances is violated. That is, we will relax the assumption that the disturbance related to an observation is independent of the disturbance related to another observation. We call this situation serial correlation or autocorrelation. Simply put, in autocorrelation Cov(εt, εs) ≠ 0 for t ≠ s where t and s are two time periods. Autocorrelation most often occurs in time series data where the observation at a given point in time is dependent on the observations from the previous time periods
The texts by Greene (2003, Chapter 12), Meyers (1990, Chapter 7), and Verbeek (2004, Chapter 4) offer a good discussion on autocorrelation models. Brocklebank and Dickey (2003) offer a thorough treatment of how SAS can be used to fit autocorrelation models.
Autocorrelation in regression models often occurs when models are misspecified or when variables are mistakenly omitted from the model. In the omitted variable case, unobserved or omitted variables that are correlated over time are now absorbed in the error term, causing autocorrelation. As an example, consider the gasoline consumption data in Greene (2003). Gasoline consumption along with measurements on other variables was observed from 1960 to 1995. Note that this data was analyzed in Chapter ...