From the Preface The first edition of this book was written mainly for audiences with physical science and engineering backgrounds. Nevertheless, it reached some readers with economic and management science training. Analytical training of graduate students in economics and management sciences had progressed much in the last 20 years, and many new research results and optimization algorithms have also become available. My own interest in the meantime has shifted to the analysis of dynamics and optimization problems of economic and management science origin. With these developments and changes, I decided to rewrite much of the first edition to make it more accessible to graduate students and professionals in social sciences. I have also incorporated some new analytic tools that I deem useful in analyzing the dynamic and stochastic problems which confront these readers. I hope that my efforts successfully bring intertemporal optimization problems closer to economics professionals. New topics introduced into this second edition appear mostly in Chapters 2, 4, 5, 6, and 8. Martingales and martingale differences are introduced early in Chapter 2. Some limit theorems and asymptotic properties of linear state space models driven by martingale differences are presented. Because many excellent books are available on martingales and their limit theorems, derivations and proofs are mostly sketchy, and readers are referred to these sources. The results in Chapteer 2 are applied in Chapters 5, 6, and 8, among other places. The notion of dynamic aggregation and its relation to cointegration and error-correction models are developed in Chapter 4. Some recursive parameter estimation schemes and their statistical properties are included in Chapters 5 and 6. Here again, books devoted entirely to these topics are available in the literature, and much had to be omitted to keep the second edition to a manageable size. In an appendix to Chapter 7, a potentially very powerful tool in proving convergence of adaptive schemes is outlined. Rational expectations models and their solution methods are developed in Chapter 8 because of their wide-spread interest to economists. A very important class of problems in sequential decision problems revolves around questions of approximating nonlinear dynamics or more generally complex situations with a sequence of less complex ones. Chapter 9 does not begin to do justice to this class of problems but is included as being suggestive of works to be done. When I first started contemplating the revision of the first edition, I benefited from a list of excellent suggestions from Rick van der Ploeg, though I did not necessarily incorporate all of his suggestions. Conversations with Thomas Sargent and Victor Solo were useful in organizing the material into the form of the second edition. I also benefited from discussions with Hashem Pesaran and correspondences with L. Broze in finalizing Chapter 8. Some material in this book was used as lecture notes in a graduate course in the Department of Economics, University of California, Los Angeles, the winter quarter of 1987. I thank the participants in the course for many useful comments. Key Features * This major revision of the First Edition addresses optimization problems stated in stochastic difference equations, which often contain uncertain or randomly varying parameters * Presents a set of concepts and techniques useful in analyzing or controlling stochastic dynamic processes, with possible incompletely specified characteristics * It discusses basic system properties such as: * Stability and observability * Dynamic programming formulations of optimal and adaptive control problems * Parameter estimation schemes and their convergence behavior * Solution methods for rational expectations models using martingale differences

Optimization of Stochastic Systems: Topics in Discrete-Time Dynamics (ECONOMIC THEORY, ECONOMETRICS, AND MATHEMATICAL ECONOMICS)

Computers & Technology

AOKI, Masanao

Computer Science

Academic Pr

In this book, the author adopts a state space approach to time series modeling to provide a new, computer-oriented method for building models for vector-valued time series. This second edition has been completely reorganized and rewritten. Background material leading up to the two types of estimators of the state space models is collected and presented coherently in four consecutive chapters. New, fuller descriptions are given of state space models for autoregressive models commonly used in the econometric and statistical literature. Backward innovation models are newly introduced in this edition in addition to the forward innovation models, and both are used to construct instrumental variable estimators for the model matrices. Further new items in this edition include statistical properties of the two types of estimators, more details on multiplier analysis and identification of structural models using estimated models, incorporation of exogenous signals and choice of model size. A whole new chapter is devoted to modeling of integrated, nearly integrated and co-integrated time series.

State space modeling of time series

Business & Money

Economics

Springer, Verlag

Optimal Control and System Theory in Dynamic Economic Analysis (Dynamic Economics: 1)

Science & Math

Physics

North-Holland Pub. Co.

New Approaches to Macroeconomic Modeling: Evolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects

This book contributes substantively to the current state of the art of macroeconomic modeling by providing a method for modeling large collections of heterogeneous agents subject to nonpairwise externality called field effects, i.e. feedback of aggregate effects on individual agents or agents using state-dependent strategies. Adopting a level of microeconomic description that keeps track of compositions of fractions of agents by "types" or "strategies", time evolution of the microeconomic states is described by (backward) Chapman-Kolmogorov equations.

Cambridge University Press

Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents

This book analyzes how a large but finite number of agents interact, and what sorts of macroeconomic statistical regularities or patterns may evolve from these interactions. By keeping the number of agents finite, the book examines situations such as fluctuations about equilibria, multiple equilibria and asymmetrical cycles of models which are caused by model states stochastically moving from one basin of attraction to another. All of these are not tractable using traditional deterministic modeling approaches. The book also discusses how agents may form clusters with stationary distributions of cluster sizes. These have important applications in analyzing volatilities of asset returns.

This book contributes substantively to the current state of the art of macroeconomic modeling by providing a method for modeling large collections of heterogeneous agents subject to nonpairwise externality called field effects, i.e. feedback of aggregate effects on individual agents or agents using state-dependent strategies. Adopting a level of microeconomic description that keeps track of compositions of fractions of agents by "types" or "strategies", time evolution of the microeconomic states is described by (backward) Chapman-Kolmogorov equations.

The authors treat macroeconomic models as composed of large numbers of micro-units or agents of several types and explicitly discuss stochastic dynamic and combinatorial aspects of interactions among them. In mainstream macroeconomics sound microfoundations for macroeconomics have meant incorporating sophisticated intertemporal optimization by representative agents into models. Optimal growth theory, once meant to be normative, is now taught as a descriptive theory in mainstream macroeconomic courses. In neoclassical equilibria flexible prices led the economy to the state of full employment and marginal productivities are all equated. Professors Aoki and Yoshikawa contrariwise show that such equilibria are not possible in economies with a large number of agents of heterogeneous types. They employ a set of statistical dynamical tools via continuous-time Markov chains and statistical distributions of fractions of agents by types available in the new literature of combinatorial stochastic processes, to reconstruct macroeconomic models.

Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes (Japan-US Center UFJ Bank Monographs on International Financial Markets)

Yoshikawa, Hiroshi

The authors treat macroeconomic models as composed of large numbers of micro-units or agents of several types and explicitly discuss stochastic dynamic and combinatorial aspects of interactions among them. In mainstream macroeconomics sound microfoundations for macroeconomics have meant incorporating sophisticated intertemporal optimization by representative agents into models. Optimal growth theory, once meant to be normative, is now taught as a descriptive theory in mainstream macroeconomic courses. In neoclassical equilibria flexible prices led the economy to the state of full employment and marginal productivities are all equated. Professors Aoki and Yoshikawa contrariwise show that such equilibria are not possible in economies with a large number of agents of heterogeneous types. They employ a set of statistical dynamical tools via continuous-time Markov chains and statistical distributions of fractions of agents by types available in the new literature of combinatorial stochastic processes, to reconstruct macroeconomic models.

In seminars and graduate level courses I have had several opportunities to discuss modeling and analysis of time series with economists and economic graduate students during the past several years. These experiences made me aware of a gap between what economic graduate students are taught about vector-valued time series and what is available in recent system literature. Wishing to fill or narrow the gap that I suspect is more widely spread than my personal experiences indicate, I have written these notes to augment and reor ganize materials I have given in these courses and seminars. I have endeavored to present, in as much a self-contained way as practicable, a body of results and techniques in system theory that I judge to be relevant and useful to economists interested in using time series in their research. I have essentially acted as an intermediary and interpreter of system theoretic results and perspectives in time series by filtering out non-essential details, and presenting coherent accounts of what I deem to be important but not readily available, or accessible to economists. For this reason I have excluded from the notes many results on various estimation methods or their statistical properties because they are amply discussed in many standard texts on time series or on statistics.

Notes on Economic Time Series Analysis: System Theoretic Perspectives (Lecture Notes in Economics and Mathematical Systems, 220)

Springer

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Books by AOKI, Masanao

See the best price to sell, buy, or rent books by AOKI, Masanao. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Optimization of Stochastic Systems: Topics in Discrete-Time Dynamics (ECONOMIC THEORY, ECONOMETRICS, AND MATHEMATICAL ECONOMICS)

State space modeling of time series

Optimal Control and System Theory in Dynamic Economic Analysis (Dynamic Economics: 1)

New Approaches to Macroeconomic Modeling: Evolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects

Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents

New Approaches to Macroeconomic Modeling: Evolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects

Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents

Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes (Japan-US Center UFJ Bank Monographs on International Financial Markets)

Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes (Japan-US Center UFJ Bank Monographs on International Financial Markets)

Notes on Economic Time Series Analysis: System Theoretic Perspectives (Lecture Notes in Economics and Mathematical Systems, 220)