Chapter 6 has developed regression techniques for modelling relationships between non-integrated time series. As we have seen in earlier chapters, however, many financial time series are integrated, often able to be characterised as I(1) processes, and the question thus arises as to whether the presence of integrated variables affects our standard regression results and conventional procedures of inference.

To this end, section 1 investigates this question through the analysis of spurious regressions between integrated time series. This leads naturally on to the concept of cointegration, which is introduced in section 2. Testing for cointegration in regression models is discussed in section 3 and the estimation of cointegrating regressions is the subject material of section 4. Section 5 considers VARs containing integrated and, possibly, cointegrated variables, which enables us to develop the vector error correction model (VECM) framework. Causality testing in VECMs is discussed in section 6 and alternative estimation methods in section 7. Finally, impulse response functions are analysed within a VECM framework in section 8.

Spurious regression

We begin by considering the simulation example analysed by Granger and Newbold (1974) in an important article examining some of the likely empirical consequences of nonsense, or spurious, regressions in econometrics.