Abstract
This chapter investigates the consequences of nonstationarity (in the form of unit roots in the assumed ARMA representation of a time series) for the econometric methodologies that have been developed in Chapters 13. Section 4.1 defines unit root processes and explains what it means to detrend such processes. Section 4.2 gives information about problems caused by the use of nonstationary, trending series in regression analysis. Section 4.3 describes the tests that can be used to verify the presence of a unit root in a series, in particular the Dickey-Fuller and the augmented Dickey-Fuller tests, along with those proposed by Philips and Perron and by Kwiatkowski, Phillips, Schmidt, and Shin. Finally, Section 4.4 introduces the concept of cointegration; it explains how to test for the presence of cointegrated variables, and the fact that the presence of cointegration always implies a vector error-correction model representation.
Keywords: Nonstationarity; unit root; deterministic trend; cointegration; vector error-correction model; common stochastic trends
Essentials of Time Series for Financial Applications 