Phoebus J. Dhrymes - Böcker

This book addresses the need for a high-level analysis of unit roots and cointegration. "Time Series, Unit Roots, and Cointegration" integrates the theory of stationary sequences and issues arising in the estimation of their parameters, distributed lags, spectral density function, and cointegration. The book also includes topics that are important for understanding recent developments in the estimation and testing of cointegrated nonstationary sequences, such as Brownian motion, stochastic integration, and central limit theorems. It explores an important topic in time-series econometrics. It addresses the need for a high-level analysis of unit roots and cointegration. It is written by an excellent expositor.

This book is intended for second year graduate students and professionals who have an interest in linear and nonlinear simultaneous equations mod­ els. It basically traces the evolution of econometrics beyond the general linear model (GLM), beginning with the general linear structural econo­ metric model (GLSEM) and ending with the generalized method of mo­ ments (GMM). Thus, it covers the identification problem (Chapter 3), maximum likelihood (ML) methods (Chapters 3 and 4), two and three stage least squares (2SLS, 3SLS) (Chapters 1 and 2), the general nonlinear model (GNLM) (Chapter 5), the general nonlinear simultaneous equations model (GNLSEM), the special ca'3e of GNLSEM with additive errors, non­ linear two and three stage least squares (NL2SLS, NL3SLS), the GMM for GNLSEIVl, and finally ends with a brief overview of causality and re­ lated issues, (Chapter 6). There is no discussion either of limited dependent variables, or of unit root related topics. It also contains a number of significant innovations. In a departure from the custom of the literature, identification and consistency for nonlinear models is handled through the Kullback information apparatus, as well as the theory of minimum contrast (MC) estimators. In fact, nearly all estimation problems handled in this volume can be approached through the theory of MC estimators. The power of this approach is demonstrated in Chapter 5, where the entire set of identification requirements for the GLSEM, in an ML context, is obtained almost effortlessly, through the apparatus of Kullback information.

For sometime now, I felt that the evolution of the literature of econo­ metrics had mandated a higher level of mathematical proficiency. This is particularly evident beyond the level of the general linear model (GLM) and the general linear structural econometric model (GLSEM). The problems one encounters in nonlinear econometrics are not easily amenable to treatment by the analytical methods one typically acquires, when one learns about probability and inference through the use of den­ sity functions. Even in standard traditional topics, one is often compelled to resort to heuristics; for example, it is difficult to prove central limit theorems for nonidentically distributed or martingale sequences, solely by the use of characteristic functions. Yet such proofs are essential, even in only moderately sophisticated classroom exposition. Unfortunately, relatively few students enter a graduate economics de­ partment ready to tackle probability theory in measure theoretic terms. The present volume has grown out of the need to lay the foundation for such discussions. The motivating forces were, chiefly, (a) the frustration one encounters in attempting to communicate certain concepts to stu­ dents wholly in analytic terms; and (b) the unwillingness of the typical student to sit through several courses in mathematics departments, in order to acquire the requisite background.

This book is intended for second year graduate students and professionals who have an interest in linear and nonlinear simultaneous equations mod­ els. It basically traces the evolution of econometrics beyond the general linear model (GLM), beginning with the general linear structural econo­ metric model (GLSEM) and ending with the generalized method of mo­ ments (GMM). Thus, it covers the identification problem (Chapter 3), maximum likelihood (ML) methods (Chapters 3 and 4), two and three stage least squares (2SLS, 3SLS) (Chapters 1 and 2), the general nonlinear model (GNLM) (Chapter 5), the general nonlinear simultaneous equations model (GNLSEM), the special ca'3e of GNLSEM with additive errors, non­ linear two and three stage least squares (NL2SLS, NL3SLS), the GMM for GNLSEIVl, and finally ends with a brief overview of causality and re­ lated issues, (Chapter 6). There is no discussion either of limited dependent variables, or of unit root related topics. It also contains a number of significant innovations. In a departure from the custom of the literature, identification and consistency for nonlinear models is handled through the Kullback information apparatus, as well as the theory of minimum contrast (MC) estimators. In fact, nearly all estimation problems handled in this volume can be approached through the theory of MC estimators. The power of this approach is demonstrated in Chapter 5, where the entire set of identification requirements for the GLSEM, in an ML context, is obtained almost effortlessly, through the apparatus of Kullback information.

For sometime now, I felt that the evolution of the literature of econo­ metrics had mandated a higher level of mathematical proficiency. This is particularly evident beyond the level of the general linear model (GLM) and the general linear structural econometric model (GLSEM). The problems one encounters in nonlinear econometrics are not easily amenable to treatment by the analytical methods one typically acquires, when one learns about probability and inference through the use of den­ sity functions. Even in standard traditional topics, one is often compelled to resort to heuristics; for example, it is difficult to prove central limit theorems for nonidentically distributed or martingale sequences, solely by the use of characteristic functions. Yet such proofs are essential, even in only moderately sophisticated classroom exposition. Unfortunately, relatively few students enter a graduate economics de­ partment ready to tackle probability theory in measure theoretic terms. The present volume has grown out of the need to lay the foundation for such discussions. The motivating forces were, chiefly, (a) the frustration one encounters in attempting to communicate certain concepts to stu­ dents wholly in analytic terms; and (b) the unwillingness of the typical student to sit through several courses in mathematics departments, in order to acquire the requisite background.

The book also covers pseudo-inverses, solutions to systems of linear equations, solutions of vector difference equations with constant coefficients and random forcing functions, matrix differentiation, and permutation matrices.