Serial correlation in time series regression models - an introduction

Abstract

Although the expression “serial correlation” (or simply autocorrelation) may be used in relation to any variable, in traditional econometrics it is meant to refer to a particular variable or time series: that of the errors of the regression model. It has therefore a clearly negative sense in this framework: the errors of a well specified model should not be serially correlated (unless in very special circumstances). Although I have tried always to add the name of the variable to which it refers, any omission should be interpreted in the usual sense. This text is very strongly based in my teaching notes, most of them with many years as the subject has not evolved or has changed little in the last years. Anyway, I had to make a choice between many teaching materials and I chose not to address the problems of GLS and EGLS estimation. It is not that they are completely irrelevant. For instance, some of the most powerful unit root tests require GLS estimation. However, as will become clear below, I think that they are very rarely a good option to follow when one faces serial correlation problems and, given severe time restrictions, I have opted to neglect the theme. Although attractive from the computational point of view, they are only rarely a reasonable alternative to folllow. As Professor Graham Mizon noted: “autocorrelation correction: Don't!”. My hope is that the reason why such a strategy is usually awed is clearly understood with this text. With a very “classical” background but philosophy-based in the British (LSE) econometric tradition, this text draws heavily from such classical sources as those of Davidson and Mackinnon (1993), Greene (2012), Johnston and Dinardo (1998). With the inclusion of some examples of Monte Carlo simulation it is expected that some testing problems are well grasped.