Applied Time Series Analysis for the Social Sciences

8OLS and the Gauss–Markov Assumptions

Let us re‐examine what we learn about autocorrelation in introductory regression courses now that we know a little more about time series properties. This chapter introduces critiques both of standard methods for detecting autocorrelation, and of reflexively “correcting” autocorrelation with generalized least squares (GLS) approaches. While the advice in this chapter is not limited to the contents of Grayham Mizon’s 1995 paper, its gist is well‐summarized by the title: “A simple message for autocorrelation‐correctors: Don’t.”

The first section explaining autocorrelation and its consequences should be review for most readers. The second section introduces both the Durbin–Watson and Breusch–Godfrey methods of detecting autocorrelation, and evaluates the advantages and disadvantages of these statistics compared with tools like the autocorrelation function and Q statistics presented in Chapter 4.

The standard “fix” – approaches based on GLS – is presented in the third section. While a typical matrix algebra derivation is provided, a simpler presentation using lag operator algebra is also introduced and used to derive extensions of the model. The chapter concludes with two caveats regarding these approaches. The “Common Factors” critique is a reminder that the assumptions underpinning GLS methods are restrictive, and that the standard GLS model correcting for first‐order autocorrelation is just one special case of the autoregressive distributed ...