ABSTRACT
It is often of interest to study the impact of a known intervention upon a second variable. Examples include the impact of an increase in tobacco taxes on teenage smoking, the impact of an environmental regulation on pollution, or the impact of an advertising campaign upon sales. Denoting the variable that is believed to be affected by the known intervention by yt, then the relationship
(8.1) can be used to not only model the impact of the intervention but also to capture the impact of other secondary factors affecting yt. In Equation 8.1 X't is a row vector of independent variables including a dummy variable representing the impact of the intervention, β is a column vector of param eters, and the et is assumed to be independent and identically distributed random variables with mean 0 and variance σ2. Thus, Equation 8.1 is the standard multiple regression model including the use of dummy variables to capture the affect of the known intervention. It is often the case that yt is a time series, a sequence of data arranged sequentially in time. Ex perience with time series data suggests that the data for any time point are often correlated with its own past values, in other words, yt is often correlated with yt-k where k is a positive integer. This property is termed autocorrelation. When yt is autocorrelated, it is likely that the errors et in Equation 8.1 will also be autocorrelated, violating one of the assumptions of the standard multiple regression model. Thus, when model 1 is used with time series data, it is prudent to be prepared for the possibility of autocorrelated error terms.
