UNIT ROOT AND COINTEGRATION TESTING: GUEST EDITORSʹ INTRODUCTION

By pointing out the spurious regression problem, Granger and Newbold ~1974! have shown the importance of stochastic trends in time series data in the context of linear regression models+ At the time, removing trends by differencing was already common practice in univariate time series modeling as part of the Box–Jenkins approach ~Box and Jenkins, 1976!+ These new developments, however, emphasized the importance of autoregressive ~AR! unit roots and motivated the development of statistical procedures for their detection+ Dickey and Fuller ~1979! and Fuller ~1976! were pioneers in developing tests for unit roots that became widely used+ The foundation of asymptotic theory for regressions involving stochastic trends was led by Phillips ~1986, 1987! with the introduction of the functional limit theory, weak convergence methods, convergence to stochastic integrals, nonparametric unit root testing, and continuous record asymptotics+ Phillips and Durlauf ~1986! extended some of these results to the multivariate setting by presenting the multivariate invariance principles and the asymptotic theory of multivariate nonstationary and cointegrating regressions+ These contributions provided the asymptotic tools that have served as the basis for most of the limit results derived in the context of unit root nonstationarity, and they have stimulated extensive subsequent research+ Over the last 30 years many other important contributions were made, of which the following are of particular relevance+ Augmented Dickey–Fuller ~ADF! tests