Estimation Of Stochastic Input Output Models

This monograph is a revision of my Indiana University doctoral disserta tion which was completed in April, 1975. Thanks are, therefore, due to the members of my doctoral committee: Saul Pleeter (Chairman), David J. Behling, R. Jeffery Green, Richard L. Pfister, and Elmus Wicker for their helpful comments on previous versions of the manuscript. In addition, I am indebted to the Division of Research and to the Office of Research and Advanced Studies at Indiana University for financial support. As the reader will observe, the techniques developed in Chapters 3 and 4 of this monograph are illustrated using input-output data from West Virginia. These data were generously made available by William H. Miernyk, Director of the Regional Research Institute at West Virginia University. I also wish to acknowledge the Bureau of Business and Eco nomic Research at Arizona State University for providing two research assistants, Kevin A. Nosbisch and Tom R. Rex, who aided in processing the West Virginia data. A third research assistant, Phillip M. Cano, also worked on this project as part of an independent study program taken under my direction during the spring semester of 1975. Finally, I must thank Mary Holguin and Margaret Shumway who expertly typed the final copy of the manuscript. Despite the efforts of all the individuals mentioned above, I assume responsibility for any errors which may remain.

This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.

Stochastic Models: Estimation and Control: v. 2

In September 1977 a "Regional Science Symposium" was held at the Faculty of Economics of the University of Goningen in the Netherlands. The impetus in organizing this symposium was the recent estab lishmen t at the F acuIty of Economics of a group engaged in teaching and research within the field of regional science. The aim of the symposium was to familiarize university members with regional science and to introduce the new group to both the national and international scene. Two separate topics of potential interest to both researchers and policy-makers were selected. The first theme, spatial inequalities and regional development, was chosen because of its central place in regional science. Authors from several disciplines were asked to approach this theme from a general, policy-oriented point of view. This ensured the spotlighting of the various dimensions of spatial inequality and its implications for regional policy. The results of their efforts have been collected in a volume entitled Spatial Inequalities and Regional Development. The second theme focussed on spatial statistical analysis. This branch of statistics is a relatively new one. It is receiving growing attention from researchers in the field of applied regional science. The conference dealing with this topic concentrated on recent research results related to the use of appropriate statistical and econometric methods for analyzing spatial data. The papers con cerned have been collected in another volume, entitled Exploratory and Explanatory Statistical Analysis of Spatial Data.

In recent years the development of spatial referencing techniques in com puter-based information systems has enormously increased the opportuni ties that exist for the treatment and presentation of both point and interaction data. The extent of this increase has drawn attention to the need for special aggregation and clustering procedures to be developed which enable data to be grouped in an efficient way for analytical pur poses with a minimum loss of detail. In the case of interaction data, economy of representation is particularly important as the analysis is further complicated by the two-way directionality that is inherent in each data set. Procedural rules of this kind are needed not only for descriptive analy sis and spatial accounting but also for hypothesis testing and the develop ment of operational models of spatial interaction. Yet the importance of spatial representation in this kind of research has only recently been fully understood. The first generation of urban development models that were developed in Europe and North America during the 1960's often treated matters of zoning system specification very casually, even though in some cases this imposed severe limits on the interpretation of their findings and it was not until the Centre for Environmental Studies/Cheshire project (Barras et al. , 1971) that a serious attempt was made to put forward general principles which could be used as guidelines in future work.