In a recent paper, Cavaliere et al., [Cavaliere G, 2012] develop bootstrap implementations of the popular likelihood-based co-integration rank tests and associated sequential rank determination procedures of Johansen [Johansen S, 1996]. By using estimates of the parameters of the underlying co-integrated VAR model obtained under the restriction of the null hypothesis, they show that consistent bootstrap inference can be obtained for processes whose deterministic component is either zero, a restricted constant or a restricted trend. In this article, we extend their bootstrap approach to allow the deterministic component to follow the practically relevant cases of either an unrestricted constant or an unrestricted trend from Johansen [Johansen S, 1996]. A full asymptotic theory is provided for these two cases, establishing the asymptotic validity of the resulting bootstrap tests. Our results, taken together with those in Cavaliere et al., [Cavaliere G, 2012], therefore show that the bootstrap approach based on imposing the reduced rank null hypothesis is valid for all five of these deterministic settings. Monte Carlo evidence demonstrates the improvements that the proposed bootstrap methods can deliver over the corresponding asymptotic procedures.

This valuable text provides a comprehensive introduction to VAR modelling and how it can be applied. In particular, the author focuses on the properties of the Cointegrated VAR model and its implications for macroeconomic inference when data are non-stationary. The text provides a number of insights into the links between statistical econometric modelling and economic theory and gives a thorough treatment of identification of the long-run and short-run structure as well as of the common stochastic trends and the impulse response functions, providing in each case illustrations of applicability. This book presents the main ingredients of the Copenhagen School of Time-Series Econometrics in a transparent and coherent framework. The distinguishing feature of this school is that econometric theory and applications have been developed in close cooperation. The guiding principle is that good econometric work should take econometrics, institutions, and economics seriously. The author uses a single data set throughout most of the book to guide the reader through the econometric theory while also revealing the full implications for the underlying economic model. To test ensure full understanding the book concludes with the introduction of two new data sets to combine readers understanding of econometric theory and economic models, with economic reality.

A comprehensive review of unit roots, cointegration and structural change from a best-selling author.

Aimed at graduates and researchers in economics and econometrics, this is a comprehesive exposition of Soren Johansen's remarkable contribution to the theory of cointegration analysis.

This book is designed for self study. The reader can apply the theoretical concepts directly within R by following the examples.