Dynamic Feature Space Modelling, Filtering and Self-Tuning Control of Stochastic Systems: A Systems Approach with Economic and Social Applications

ISBN-13: 9783540156543 / Angielski / Miękka / 1985 / 184 str.

Pieter W. Otter

Opis

The literature on systems seems to have been growing almost expo nentially during the last decade and one may question whether there is need for another book. In the author's view, most of the literature on 'systems' is either technical in mathematical sense or technical ifF engineering sense (with technical words such as noise, filtering etc. ) and not easily accessible to researchers is other fields, in particular not to economists, econometricians and quantitative researchers in so cial sciences. This is unfortunate, because achievements in the rather 'young' science of system theory and system engineering are of impor tance for modelling, estimation and regulation (control) problems in other branches of science. State space mode iing; the concept of ob servability and controllability; the mathematical formulations of sta bility; the so-called canonical forms; prediction error e timation; optimal control and Kalman filtering are some examples of results of system theory and system engineering which proved to be successful in practice. A brief summary of system theoretical concepts is given in Chapter II where an attempt has been made to translate the concepts in to the more 'familiar' language used in econometrics and social sciences by means of examples. By interrelating concepts and results from system theory with those from econometrics and social sciences, the author has attempted to narrow the gap between the more technical sciences such as engi neering and social sciences and econometrics, and to contribute to either side."

Spis treści

I: Introduction.- II: Elements of System Theory.- 2.1 Definitions of Dynamic Input-Output and State Space Models.- 2.2 Observability, Reconstructability and Controllability.- 2.3 Realization Theory.- 2.4 Canonical Forms.- 2.5 Stability.- A: Modelling, Filtering and Identification.- III: Feature Space Modelling.- 3.1 Introduction.- 3.2 A Linear Stochastic Dynamic Model with Feature Space.- 3.3 Models with Factor Space.- 3.4 Models with Canonical Space.- 3.5 Singular Value Decomposition and Canonical Correlation.- 3.6 Models with State Space: Balanced Realizations and Model Reduction.- 3.7 State Space Representation of Multivariate Time-Series.- 3.8 Regression Models with Parameter Space.- IV: Discrete Kalman Filtering.- 4.1 Derivation of the Filter.- 4.2 The Kaiman Filter applied to the Classical Linear Regression Model with Constant Parameters.- 4.3 The Kaiman Filter considered to be a Bayesian Estimation Procedure and some (Asymptotic) Properties.- 4.4 Stability of the Discrete Kaiman Filter and its Steady State.- 4.5 Prediction Errors (Innovations).- 4.6 Divergence of the Filter.- V: Parameter Identifiability, Prediction Error Estimation And Model Check.- 5.1 Parameter Identifiability.- 5.2 Stochastic Reconstructability and Parameter Identifiability.- 5.3 Prediction Error Estimation.- 5.4 A Non-Linear Minimization Procedure.- 5.5 Prediction Error Estimation of the (LSF) and (LRF) model.- 5.6 Prediction Error Estimation and Jöreskog’s LISREL-Procedure.- 5.7 Likelihood Ratio and Model Check.- 5.8 Structure Selection.- VI: Economic Applications.- 6.1 Regression.- 6.2 A Case Study.- 6.3 Univariate Time-Series Modelling.- 6.4 Multivariate Time-Series Modelling.- 6.5 Structural Modelling..- 6.6 Models with ‘Unobservables’.- B: Control.- VII: Self-Tuning Control.- 7.1 Introduction.- 7.2 Linear Quadratic Gaussian (LQG) Control.- 7.3 Minimum Variance (MV) Control.- 7.4 Duality of Estimation (Filtering) and Control.- 7.5 Estimation in Closed Loop.- 7.6 Self-Tuning Control.- 7.7 Self-Tuning Control of a Macro-Economic System.- Appendix: Solution of the Linear Matrix A X B + C = X and the Are.- References.