Applied Time Series Analysis for the Social Sciences

4Properties of Time Series: Autocorrelation

4.1 Rethinking Autocorrelation

In introductory regression courses, autocorrelation is introduced as a potential problem afflicting the error term in a regression model such as this

(4.1)

and our attention is frequently restricted to first-order autocorrelation, i.e., correlation between and .

It is, however, more useful to recognize that in typical time series applications, the dependent variable Y _t is autocorrelated – e.g., Y _t is correlated with . Consider a stock price or voters’ approval rating of a politician. In the absence of a dramatic event, we would be surprised if there were a dramatic change from one day to the next – that is, we expect today’s value, Y _t , to be relatively close to yesterday’s value, . We may not be sure of the precise reasons for this – for example, whether voters simply maintain fixed assessments of politicians until shaken by a random event, or if the assessments tend to be stable in the short run ...