Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Excerpt

Throughout the period of preparing this monograph I have had the pleasure of collaborating with Katarina Juselius, who introduced me to the topic of cointegration by asking me to give some lectures on the basic paper by Clive Granger (1983). Since then we have worked on developing the theory in close contact with the applications, and the results we have obtained have been driven by the need to understand the variation of economic data. Thus the theory has been forced upon us by the applications, and the theory has suggested new questions that could be asked in practice. I feel fortunate in having had the opportunity for this type of collaboration, and would like to use this opportunity to thank Katarina for being so inspiring.

The monograph is on the mathematical statistical analysis of models that have turned out to be helpful in the analysis of economic data. I have used two economic examples that have been analysed in the literature, so that the statistical concepts can be illustrated by some economic concepts, but the main emphasis is on the statistical analysis. If the reader is more interested in the applications of the techniques, I must refer to the many publications on the modelling of economic data using cointegration that have been published.

It is my hope that there is still room for a thorough exposition of the details of this theory even if the method has already found its way into textbooks in econometrics, see for instance Reinsel (1991), Banerjee et al. (1993), Hamilton (1994), and Lütkepohl (1991). There are a number of collections of papers that deal almost exclusively with cointegration, see Engle and Granger (1991), and special issues of Oxford Bulletin of Economics and Statistics (1990, 1992) and Journal of Policy Modelling (1993).

The monograph does not cover all aspects of cointegration but it is my hope that by studying some topics in detail one can understand the further developments. Thus I have left out the important work by Phillips (1991), Park (1992), Stock (1987) Stock and Watson (1988, 1993) to mention a few. These papers deal with cointegration from a different perspective which one can summarize as cointegrating regressions, that is, they study how the usual regression estimator can be improved in view of the underlying stochastic model. Phillips (1991) also gives a statistical theory for a semi-parametric model for cointegration, but the approach taken here is entirely parametric.

In 1989 we were invited by Domenico Sartore to present the theory and application of cointegration at a summer school in Bagni di Lucca organized by Centro Interuniversitario di Econometria.

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