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Continuous-time econometrics is no longer an esoteric subject although most still regard it as such, so much so that it is hardly mentioned in standard textbooks on econometrics. Thanks to the work done in the last 20 years, both the theoretical and the applied side are by now well developed. Methods of estimation have been theoretically elaborated and practically implemented through computer programs. Continuous-time macroeconometric models for different countries have been constructed, estimated and used. Being myself involved in these developments, it was with great pleasure that I accepted the invitation to organize a session on continuous-time econometrics in the context of the International Symposium on Economic Modelling (jointly organized by the University of Urbino and the book series International Studies in Economic Modelling, and co-sponsored by the Consiglio Nazionale delle Ricerche). The reaction of 'continuists' from all over the world was so enthusiastic that I was able to arrange two sessions, one on the theory and the other on the applications. The symposium was held in Urbino on 23-25 July 1990. The papers presented in Urbino have been revised in the light of the discussion at the symposium and the referees' comments. Hence, what is published here should become another standard reference in the field of continuous-time econometrics.
. The organizers of the ninth symposium, which produced the current proceedings volume, were Claude Hillinger at the University of Munich, Giancarlo Gandolfo at the University of Rome "La Sapienza," A. R. Bergstrom at the University of Essex, and P. C. B. Phillips at Yale University.
This unique book provides an overview of continuous time modeling in the behavioral and related sciences. It argues that the use of discrete time models for processes that are in fact evolving in continuous time produces problems that make their application in practice highly questionable. One main issue is the dependence of discrete time parameter estimates on the chosen time interval, which leads to incomparability of results across different observation intervals. Continuous time modeling by means of differential equations offers a powerful approach for studying dynamic phenomena, yet the use of this approach in the behavioral and related sciences such as psychology, sociology, economics and medicine, is still rare. This is unfortunate, because in these fields often only a few discrete time (sampled) observations are available for analysis (e.g., daily, weekly, yearly, etc.). However, as emphasized by Rex Bergstrom, the pioneer of continuous-time modeling in econometrics, neither human beings nor the economy cease to exist in between observations. In 16 chapters, the book addresses a vast range of topics in continuous time modeling, from approaches that closely mimic traditional linear discrete time models to highly nonlinear state space modeling techniques. Each chapter describes the type of research questions and data that the approach is most suitable for, provides detailed statistical explanations of the models, and includes one or more applied examples. To allow readers to implement the various techniques directly, accompanying computer code is made available online. The book is intended as a reference work for students and scientists working with longitudinal data who have a Master's- or early PhD-level knowledge of statistics.
Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.
The Journal of Econometrics is designed to serve as an outlet for important new research in both theoretical and applied econometrics. The scope of the Journal includes papers dealing with estimation and other methodological aspects of the application of statistical inference to economic data, as well as papers dealing with the application of econometric techniques to substantive areas of economics. Econometric research in the traditional divisions of the discipline or in the newly developing areas of social experimentation are decidedly within the range of the Journal's interests.
This study is a revised version of my doctoral dissertation at the Economics Department of the University of Munich. I want to take the opportunity to express my gratitude to some people who have helped me in my work. My greatest thanks go to the supervisor of this dissertation, Professor Claude Billinger. Bis ideas have formed the basis of my work. Be permanently sup ported it with a host of ideas, criticism and encouragement. Furthermore, he provided a stimulating research environment at SEMECON. This study would not have been possible in this form without the help of my present and former colleagues at SEMECON. I am indebted to Rudolf Kohne-Volland, Monika Sebold-Bender and Ulrich Woitek for providing soft ware and guidance for the data analysis. Discussions with them and with Thilo Weser have helped me to take many hurdles, particularly in the early stages of the project. My sincere thanks go to them all. I had the opportunity to present a former version of my growth model at a workshop of Professor Klaus Zimmermann. I want to thank all the parti cipants for their helpful comments. I also acknowledge critical and constructive comments from an anonymous referee. Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I. Methodology 1. Importance of Stylized Facts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Limitations of statistical testing. . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Evaluating economic models. . . . . . . . . . . . . . . . . . .. . . . 11 . . . . . . 2. Further Methodological Issues . . . . . . . . . . . . . . . . . .. . . . 13 . . . . . .