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Likelihood-based inference in cointegrated vector autoregressive models. (English) Zbl 0928.62069

Oxford: Oxford Univ. Press. xii, 267 p. (1995).
This 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 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 statistical 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. 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. (From the preface.)
Contents: Part I, The statistical analysis of cointegration. 1. Introduction; 2. The vector autoregressive model; 3. Basic definitions and concepts; 4. Cointegration and representation of integrated variables; 5. The I(1) models and their interpretation; 6. The statistical analysis of I(1) models; 7. Hypothesis testing for the long run coefficients \(\beta\); 8. Partial systems and hypotheses on \(\alpha\); 9. The I(2) model and a test for I(2).
Part II, The probability analysis of cointegration. 10. Probability properties of I(1) processes; 11. The asymptotic distribution of the test for cointegrating rank; 12. Determination of cointegrating rank; 13. Asymptotic properties of the estimators; 14. The power function of the the test for cointegrating rank under local alternatives; 15. Simulations and tables.
Part III, Appendices. A. Some mathematical results; B. Weak convergence of probability measures on \(\mathbf R^{p}\) and \(\mathbf C[0,1]\).

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
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