Part II - Unit roots and cointegration

Summary

This part contains five chapters that form the core material that needs to be understood to follow the rest of the book.

Chapter 3 gives a brief introduction to Wiener processes. We do not go into these in great detail because we do not go into details of the derivations of asymptotic distributions. Those interested in these can refer to the source material. (Many empirical researchers do not need the derivations.) We next discuss the importance of scaling factors in the derivation of asymptotic distributions. Next we discuss the Dickey-Fuller (DF) distribution and the DF tests, the ADF test and the problem of selection of lag length (a problem that needs special attention). Next we discuss the Phillips-Perron (PP) tests, Sargan-Bhargava tests, variance ratio tests, and finally forecasting problems.

Although often used, the ADF and PP tests are useless in practice and should not be used. Some useful modifications of these tests are discussed in chapter 4. The material covered in this chapter forms the basis of all the modifications discussed in the next chapter.

Chapter 4 considers several issues in unit root testing. The reason why there are so many unit root tests is that there is no uniformly powerful test for the unit root hypothesis. We discuss several of the tests for completeness. Some of them are not worth considering but they are all promoted by the respective authors and the Nelson–Plosser data set is used as a guinea pig for every new test suggested.