A Primer on Unit-Roots and Cointegration¤

The analysis of unit-root processes and cointegrated systems has played a prominent role in econometrics and macroeconomics in the last decade, with applications to diverse ¯elds such as macroeconomics, ¯nance, economic history, international economics, etc. The reasons for such a rapid expansion of the subject are its strong intuitive appeal and its highly involved technical complexity. After a decade of the publication of the seminal work by Engle and Granger (1987) cointegration and unit-root techniques have become standard elements in every applied econometrician's toolkit. These notes present an introductory and informal approach to the topic at the level of any undergratuate book in econometrics. The subject well deserves a detailed and rigurous study for which there are many specialized textbooks discussed at the end of these notes. 1 Time Series. Stationarity We are assuming some familiarity with the basic theory of stationary ARMA process. In this section we review some basic concepts. A time series process is a sequence of random variables ordered in time. The notation Yt stands for the random variable variable Y at period t. A process Yt is stationary if the following conditions hold