Applied Time Series Analysis for the Social Sciences

5Autocorrelation: Univariate ARIMA Estimation and Forecasting

Chapter 4 provided a reminder that autocorrelation is a property of most time series. In the same way that two series which are both non‐stationary will be correlated with or without any reasonable causal mechanism, two time series with a common autocorrelation structure are often correlated even if there is no plausible relationship between them. This should be no surprise – remember that autocorrelation is often driven by omitted variables. Appropriately addressing autocorrelation, then, is not merely as important as addressing confounding variables in order to prevent omitted variable bias; it is frequently the same thing.

Different time series techniques address the problem in different ways. Beginning with Chapter 9, we'll see that recent approaches favor modeling autocorrelation by including enough lags of the independent and/or dependent variables to eliminate any autocorrelation in the error terms. As troubling as this strategy often seems at first to well‐trained statisticians accustomed to working with cross‐sectional data, it serves two purposes. First, it prevents the omitted variables bias that might arise from autocorrelation driven by omitted variables. Second, it facilitates the assessment of dynamic effects – the response of our dependent variable, over time, to a change in the independent variable(s) of interest. A preview of this sort of analysis will appear in the discussion of transfer functions ...