Likelihood-Based Inference In Cointegrated Vector Autoregressive Models

Since the notion of cointegration was established by Engel and Granger (1987), many statistical methods have been suggested to estimate and test cointegrated models. Undoubtedly the Gaussian likelihood–based method advocated by Johansen (1988, 1991) is one of the most popular choices among practitioners. In his 1988 paper, Johansen applied Anderson's (1951) maximum likelihood estimation procedure for reduced rank regression (RRR) models to isolate common stochastic trends in multiple time series. This was a remarkable breakthrough, which he and other authors have extended into various directions in the last decade. Johansen's approach is attractive in that it provides a unified set of tools of estimation, cointegration rank testing, and parametric hypothesis testing, based on the Gaussian likelihood for a vector autoregression (VAR). Although this book and other papers of Johansen are mostly concerned with reduced form models, the statistical information provided by his method is useful for applied econometricians, especially in fields where tractable dynamic structural models are not available. This book presents a concise yet comprehensive treatment of his methodology.