Recent Developments in Cointegration

Abstract

As an empirical econometrician, I have always strongly believed in the power of analyzing statistical models as a scientifically viable way of learning from observed data.In the aftermath of the great recession, this seems more important than ever.Most economic and econometric models in macroeconomics and finance did not seem well geared to address features in the data of key importance for the crisis.In particular, the long persistent movements away from long-run equilibrium values typical of the pre-crisis period seem crucial in this respect.Because of this, I hoped that the papers submitted to this special issue would use cointegration to address these important issues, for example by applying cointegration in models with self-reinforcing feed-back mechanisms, or by deriving new tests motivated by such empirical applications, or by dealing with near integration in the I(1) and I(2) model.No doubt, the outcome surpassed my most optimistic expectations.This special issue contains excellent contributions structured around several interconnected themes most of them addressing the above mentioned issues in one way or the other.While some of the papers are predominantly theoretical others are mainly empirical, all of them represent a good mixture of theory and applications.The theoretical papers solve problems motivated by empirical work and the empirical papers address problems using valid statistical procedures.In this sense, the collection of articles represents econometric modelling at its best.As the guest editor, I feel both proud and grateful to be able to write the editorial for so many high quality research papers.The high quality of the articles is to a significant degree a result of detailed, insightful and very useful referee reports.I would like to take the opportunity to express a deeply felt gratitude to all the reviewers having invested their precious time to check and improve the quality of the articles.Your efforts made all the difference.How to link a theoretical model with empirical evidence in a scientifically valid way is a tremendously difficult task that has been debated as long as economics and econometrics have existed.The dilemma facing an empirical economist/econometrician is that there are many economic models but only one economic reality: which of the models should be chosen?Rather than choosing one economic model and forcing it onto the data, the CVAR model structures the data based on the likelihood principle to obtain broad confidence intervals within which potentially relevant economic models should fall.This is consistent with the basic ideas of Trygve Haavelmo who, with his Nobel Prize winning monograph "The Probability Approach to Economics", can be seen as the forefather of the modern likelihood based approach to empirical economics.Juselius (2015) argues that the Cointegrated VAR model, by allowing for unit roots and cointegration, provides a solution to some of the statistical problems Trygve Haavelmo struggled with.Hoover and Juselius (2015) argue that a theory consistent CVAR scenario can be interpreted in terms of Haavelmo's notion of an "experimental design for data based on passive observations".A CVAR scenario translates all basic hypotheses of an economic model into a set of testable regularities describing long-run relations and common stochastic trends.If the basic assumptions of the theoretical model are empirically valid, then one should see these regularities in the data.As such scenarios can be formulated for competing models and then checked against data, it can be seen as a scientifically valid way of linking economic models with the statistical data.A theoretical model that passes the first check of such basic properties is potentially an

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