Spatial time series: analysis - forecasting - control
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Pion
1979
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 674 S. graph. Darst. |
| ISBN: | 0850860695 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1 The analysis of spatial systems 1
1.1 Objectives of space time systems analysis 2
1.2 The structure of systems 4
1.3 Examples of space time systems 8
1.4 Stages in analysis of spatial systems 20
1.5 Experimental design in analysis of space time systems 23
1.5.1 Choice of variables 24
1.5.2 Error sources and design 25
1.5.3 Design with experimental versus operating records 27
1.5.4 The effects of sampled observations and choice of sampling design 29
1.6 Conclusion 33
Part 1 Time Series
2 The structure of spatial systems and their representation
2.1 The structure of univariate systems 34
2.1.1 The system input 34
2.1.2 The system transfer function 37
2.1.3 The system output 45
2.2 The structure of multivariate and space time systems 51
2.2.1 The structure of multivariate systems 52
2.2.2 The structure of space time systems 57
2.3 The mathematical representation of systems 62
* 2.3.1 Difference equation representation 65
* 2.3.2 Differential equation representation 68
* 2.3.3 Transfer function integral equation representation 70
2.3.4 State space representation 72
2.4 Complications to the practical analysis of system structure 77
2.4.1 Observable and unobservable systems elements 77
2.4.2 Observability, controllability, and the minimal realisation problem 81
2.4.3 Causes and consequences of the presence of stochastic elements 86
2.5 Transfer function representation and mathematical approximants 92
2.6 Conclusion 94
3 Identification and specification of systems
3.1 System specification and inference 96
3.2 Time domain univariate identification 99
* 3.2.1 Theoretical time domain identification diagnostics 100
* 3.2.2 Estimates of time domain identification diagnostics 104
3.3 The treatment of nonstationarity and nonlinearity
in system identification 110
3.3.1 Nonlinearity 111
3.3.2 Nonstationarity 113
3.4 Cases of time domain identification 128
3.4.1 Identification of unknown system transfer function 128
3.4.2 Univariate identification of unknown output (convolution) 145
Contents
3.4 (continued)
3.4.3 Univariate identification of unknown input (deconvolution) 148
3.4.4 Identification of autoregressive moving average (ARMA) processes 150
3.4.5 System simulation 162
3.5 System identification in the frequency domain 164
3.5.1 Frequency domain univariate identification diagnostics 165
3.5.2 Aliasing and bandwidth 172
3.5.3 Estimators of the system frequency response functions 173
3.5.4 Tests of significance of spectral and cross spectral estimates 183
3.6 Cases of frequency response identification 187
3.6.1 Identification of unknown transfer functions 187
3.6.2 Identification of ARMA processes 195
3.6.3 Univariate identification: conclusion 201
3.7 Multivariate identification
3.7.1 Time domain multivariate identification diagnostics 202
3.7.2 Multivariate transfer function identification 205
3.7.3 Frequency domain multivariate identification diagnostics 208
3.7.4 Multivariate transfer function identification 210
3.8 Conclusion 212
4 Estimation of system parameters 214
4.1 Properties of parameter estimators 221
4.2 Least squares (OLS) parameter estimation 226
4.2.1 OLS estimation: univariate case 226
4.2.2 OLS estimation: multivariate case 238
4.2.3 Estimation of noise models 241
4.2.4 Assumptions of the least squares method 244
4.2.5 Difficulties in least squares estimation 245
4.3 Diagnostic checking of estimates 254
4.3.1 Diagnostic checks of models of a given order 254
4.3.2 Sequential estimation and checking 261
4.4 Recursive estimation procedure 268
4.4.1 Recursive least squares (ROLS) estimation 268
4.4.2 Recursive multivariate least squares estimation 274
4.4.3 Bayesian estimation 274
4.5 Special estimators: univariate case 277
4.5.1 Generalised least squares (GLS) estimation 278
4.5.2 Instrumental variable (IV) estimation 280
4.5.3 Stochastic approximation (including maximum likelihood)
estimation 287
4.6 Special estimators: multivariate case 298
4.6.1 Two stage least squares (2SLS) estimation 300
4.6.2 Three stage least squares (3SLS) estimation 303
4.6.3 Stochastic approximation 306
4.6.4 Canonical solutions to multivariate estimation problems 308
4.6.5 Special estimators: conclusion 313
Contents
4.7 Relations between identification and estimation 314
4.7.1 Univariate identifiability criteria 315
4.7.2 Multivariate identifiability criteria 319
4.8 Conclusion 320
5 Parameter mapping: analysis of nonstationary
and nonlinear systems
5.1 Introduction 323
5.1.1 Global analysis and parameter mapping 323
5.1.2 A representation of parameter maps 328
5.1.3 Continuous parameter models 331
5.1.4 Discontinuous parameter models 333
5.1.5 Systematic parameter models 333
5.1.6 Observability restrictions and parameter mapping:
classes of parameter dynamics 334
5.2 Recursive simulation (class 1 dynamics) 337
5.3 Parameter reconstruction (class 2 dynamics):
the Luenberger observer 341
5.4 Stochastic parameter reconstruction (class 3 dynamics):
the Kalman observer 346
5.5 Predictor corrector estimates of stochastic system equation
(class 4 and class 5 dynamics): the Kalman filter 350
5.6 Adaptive estimation of transfer function parameters
(class 6 dynamics) 357
5.6.1 Dynamic parameter estimation by window functions 359
5.6.2 Dynamic parameter estimation by error bounding 365
5.6.3 Dynamic parameter estimation by an adaptive estimator 367
5.7 Adaptive estimation of ARMA systems (class 7 dynamics) 389
5.8 Tests of significance of parameter regimes 391
5.8.1 Recursive treatment of parameter tests 392
5.8.2 Block treatment of parameter discontinuity 396
5.9 Parameter mapping: conclusion 402
Part 2 Spatial Time Series
6 Space time systems: representation, identification,
and estimation 404
6.1 The structure of space time systems 405
6.1.1 Space time system input 406
6.1.2 Space time system transfer function 408
6.1.3 Space time system output 415
6.2 The mathematical representation of space time systems 418
* 6.2.1 Space time difference equation representation 418
* 6.2.2 Space time differential equation representation 421
* 6.2.3 Space time integral equation representation 422
* 6.2.4 Space time state variable representation 423
Contents
6.3 Complications in the analysis of space time systems 425
6.3.1 Observable and unobservable space time system components 425
6.3.2 Observability, controllability, and minimal space time realisations 426
6.3.3 The effect of sampling interval constraints on space time analysis 428
6.3.4 Boundary values 430
6.3.5 The entry of stochastic elements into space time systems 431
6.4 Specification of space time systems 433
6.4.1 Estimates of space time response functions and tests of significance 435
6.4.2 System specification methods 437
6.4.3 Examples of spatial system specification 443
6.5 Estimation of space time systems 446
6.5.1 OLS estimation of space time systems 447
6.5.2 OLS estimation of space time transfer function systems 452
6.5.3 OLS estimation of space time ARMA systems 454
6.5.4 Problems in OLS estimation of spatial systems 455
6.6 Conclusion 457
7 The estimation of spatial systems and purely spatial processes
7.1 Special estimators of spatial systems 459
7.1.1 Special spatial estimators 459
7.1.2 Canonical solution 462
7.1.3 Examples of special spatial estimation 463
7.2 Parameter mapping and spatial systems 470
7.2.1 Classes of spatial parameter dynamics 471
7.2.2 Examples of spatial parameter mapping 473
7.3 Special space time processes 477
* 7.3.1 The mathematical solution of special space time systems 485
7.3.2 Nonstationarity of level in special space time systems 488
7.3.3 Identification of special space time systems 490
7.3.4 Estimation of special space time processes 497
7.4 Purely spatial processes 499
7.4.1 Purely spatial transfer function and ARMA models 503
7.4.2 Identification of purely spatial processes 504
7.4.3 Estimation of purely spatial processes 509
7.5 Conclusion 531
Part 3 Forecasting and Control
8 Forecasting and control in space time systems
8.1 The motivation for forecasting and control 533
8.1.1 Forecasting 533
8.1.2 Control 536
8.2 Mathematical forecasting in univariate systems 539
8.2.1 Forecasting with extrapolation (naive) models 539
8.2.2 Forecasting with regression models 544
8.2.3 Univariate ARMA forecasting 549
8.2.4 Univariate transfer function forecasting 552
8.2.5 Comparison of forecasting methods 557
Contents
8.3 Forecasting system changes (adaptive forecasting) 560
8.3.1 The Kalman linear predictor 561
8.3.2 Examples of Kalman linear prediction 563
8.3.3 Comparison of adaptive forecasting methods 567
8.4 Mathematical forecasting in multivariate systems 567
8.5 Spatial mathematical forecasts 568
8.6 Evaluation of forecasts 573
8.6.1 Absolute forecasting accuracy 573
8.6.2 Relative forecasting accuracy 576
8.7 Types of control systems 577
8.7.1 Suboptimal control systems 579
8.7.2 Optimal control systems 581
8.7.3 Optimal one stage quadratic control systems 585
8.7.4 Optimal T stage quadratic control systems 592
8.7.5 Space time control systems 594
8.8 Interrelations between system identification estimation
and control 600
8.8.1 Identification and estimation in controlled systems 601
8.8.2 Derivation of controllers in estimated systems 603
8.9 Forecasting and control: conclusion 610
9 Future developments in spatial analysis, forecasting,
and control
9.1 Inductive versus deductive approaches 612
9.2 Large versus small models 613
9.3 Long versus short term forecasting and model building 614
9.4 Future research directions 616
Appendices
Appendix 1.1 Notation 619
Appendix 1.2 Data sequences 623
Appendix 2.1 Simple matrix algebra 629
Appendix 2.2 Mathematical operations 636
Appendix 2.3 Observability, controllability, and minimal realisations 641
References 647
Index 667
|
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| institution | BVB |
| isbn | 0850860695 |
| language | English |
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| spelling | Bennett, Robert J. 1948- Verfasser (DE-588)129762261 aut Spatial time series analysis - forecasting - control R. J. Bennett London Pion 1979 674 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Commande, Théorie de la Commande, théorie de la ram Prévision, Théorie de la Prévision, théorie de la ram Série chronologique Série chronologique ram Control theory Prediction theory Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001484698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bennett, Robert J. 1948- Spatial time series analysis - forecasting - control Commande, Théorie de la Commande, théorie de la ram Prévision, Théorie de la Prévision, théorie de la ram Série chronologique Série chronologique ram Control theory Prediction theory Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 |
| title | Spatial time series analysis - forecasting - control |
| title_auth | Spatial time series analysis - forecasting - control |
| title_exact_search | Spatial time series analysis - forecasting - control |
| title_full | Spatial time series analysis - forecasting - control R. J. Bennett |
| title_fullStr | Spatial time series analysis - forecasting - control R. J. Bennett |
| title_full_unstemmed | Spatial time series analysis - forecasting - control R. J. Bennett |
| title_short | Spatial time series |
| title_sort | spatial time series analysis forecasting control |
| title_sub | analysis - forecasting - control |
| topic | Commande, Théorie de la Commande, théorie de la ram Prévision, Théorie de la Prévision, théorie de la ram Série chronologique Série chronologique ram Control theory Prediction theory Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Commande, Théorie de la Commande, théorie de la Prévision, Théorie de la Prévision, théorie de la Série chronologique Control theory Prediction theory Time-series analysis Zeitreihenanalyse |
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