ABSTRACT
Thus far in Part IV we have discussed problems encountered in time-series analysis: the danger of spurious regression in Chapter 10, and the problem of autocorrelation more generally in Chapter 11. We have emphasised that regression with non-stationary series is generally biased and inconsistent. Transformations to stationarity, notably differencing, create their own problems. In this chapter we will present valid procedures for obtaining regression estimates with non-stationary series. Least square estimates can be used if two non-stationary series are cointegrated, a concept we explain in section 12.2. The test for cointegration, of which examples are given in section 12.3, is to test whether the residuals from the levels regression are stationary. If these residuals are stationary then the series are cointegrated. The levels regression will then provide consistent estimates of the long-run relationship. The full dynamic model is estimated as an error correction model, which is presented in section 12.4. Section 12.5 concludes.
