Co-integration, error correction and the econometric analysis of non-stationary data / Anindya Banerjee, Juan J. Dolado, John W. Galbraith and David F. Hendry.

Notational conventions, symbols, and abbreviations, xi -- 1. Introduction and overview, 1 -- 1.1. Equilibrium relationships and the long run, 2 -- 1.2. Stationarity and equilibrium relationships, 4 -- 1.3. Equilibrium and the specification of dynamic models, 5 -- 1.4. Estimation of long-run relationships and testing for orders of integration and co-integration, 8 -- 1.5. Preliminary concepts and definitions, 10 -- 1.6. Data representation and transformations, 28 -- 1.7. Examples: typical ARMA processes, 32 -- 1.8. Empirical time series: money, prices, output, and interest Rates, 40 -- 1.9. Outline of later chapters, 42 -- Appendix, 43 -- 2. Linear transformations, error correction, and the long run in dynamic regression, 46 -- 2.1. Transformations of a simple model, 48 -- 2.2. The error-correction model, 50 -- 2.3. An example, 52 -- 2.4. Bardsen and Bewley transformations, 53 -- 2.5. Equivalence of estimates from different transformations, 55 -- 2.6. Homogeneity and the ECM as a linear transformation of the ADL, 60 -- 2.7. Variances of estimates of long-run multipliers ,61 -- 2.8. Expectational variables and the interpretation of long-run solutions, 64 -- 3. Properties of Integrated Processes, 69 -- 3.1. Spurious regression, 70 -- 3.2. Trends and random walks, 81 -- 3.3. Some statistical features of integrated processes, 84 -- 3.4. Asymptotic theory for integrated processes, 86 -- 3.5. Using Wiener distribution theory, 91 -- 3.6. Near-integrated processes, 95 -- 4. Testing for a Unit Root, 99 -- 4.1. Similar tests and exogenous regressors in the DGP, 104 -- 4.2. General dynamic models for the process of interest, 106 -- 4.3. Non-parametric tests for a unit root, 108 -- 4.4. Tests on more than one parameter, 113 -- 4.5. Further extensions, 119 -- 4.6. Asymptotic distributions of test statistics, 123 -- 5. Co-integration, 136 -- 5.1. An example, 137 -- 5.2. Polynomial matrices, 140 -- 5.3. Integration and co-integration: formal definitions and Theorems, 145 -- 5.4. Significance of alternative representations, 153 -- 5.5. Alternative representations of co-integrated variables: two examples, 153 -- 5.6. Engle-Granger two-step procedure, 157 -- 6. Regression with Integrated Variables, 162 -- 6.1. Unbalanced regressions and orthogonality tests, 164 -- 6.2. Dynamic regressions, 168 -- 6.3. Functional forms and transformations, 192 -- Appendix: Vector Brownian motion ,200 -- 7. Co-integration in individual equations, 204 -- 7.1. Estimating a single co-integrating vector, 205 -- 7.2. Tests for co-integration in a single equation, 206 -- 7.3. Response surfaces for critical values, 211 -- 7.4. Finite-sample biases in OLS estimates, 214 -- 7.5. Powers of single-equation co-integration tests, 230 -- 7.6. An empirical illustration, 236 -- 7.7. Fully modified estimation, 239 -- 7.8. A fully modified least-squares estimator, 240 -- 7.9. Dynamic specification, 242 -- 7.10. Examples, 244 -- Appendix: covariance matrices, 252 -- 8. Co-integration in systems of equations, 255 -- 8.1. Co-integration and error correction, 257 -- 8.2. Estimating co-integrating vectors in systems, 261 -- 8.3. Inference about the co-integration space, 266 -- 8.4. An empirical illustration, 268 -- 8.5. Extensions ,271 -- 8.6. A second example of the Johansen maximum likelihood Approach, 292 -- 8.7. Asymptotic distributions of estimators of co-integrating vectors in 1(1) systems, 293 -- 9. Conclusion, 299 -- 9.1. Summary, 299 -- 9.2. The invariance of co-integrating vectors, 300 -- 9.3. Invariance of co-integration under seasonal adjustment, 301 -- 9.4. Structured time-series models and co-integration, 303 -- 9.5. Recent research on integration and co-integration, 304 -- 9.6. Reinterpreting econometrics time-series problems, 307 -- References, 311 -- Acknowledgements for quoted extracts, 321 -- Author index, 323 -- Subject index, 325.