Recursive estimation and time-series analysis: an introduction for the student and practitioner
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3826576&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024521805&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 504 S. Ill., graph. Darst. |
| ISBN: | 3642219802 9783642219801 |
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| 245 | 1 | 0 | |a Recursive estimation and time-series analysis |b an introduction for the student and practitioner |c Peter C. Young |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XVII, 504 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 THE HISTORICAL CONTEXT 1
1.2 THE CONTENTS OF THE BOOK 4
1.3 SOFTWARE 7
1.4 THE AIMS OF THE BOOK 8
PART I RECURSIVE ESTIMATION OF PARAMETERS IN LINEAR REGRESSION MODELS
2 RECURSIVE ESTIMATION: A SIMPLE TUTORIAL INTRODUCTION 13 2.1 RECURSIVE
ESTIMATION OF THE MEAN VALUE OF A RANDOM VARIABLE . . .. 15 2.1.1
FILTERING INTERPRETATION OF THE RECURSIVE ALGORITHM 20 2.2 RECURSIVE
LEAST SQUARES ESTIMATION FOR A SINGLE UNKNOWN
PARAMETER 21
2.3 EXERCISES 26
2.4 SUMMARY 27
3 RECURSIVE LEAST SQUARES ESTIMATION 29
3.1 THE DETERMINISTIC RECURSIVE LINEAR LEAST SQUARES ALGORITHM 30 3.2
THE STOCHASTIC RECURSIVE LINEAR LEAST SQUARES ALGORITHM 34 3.3 SOME
CAUTIONARY COMMENTS: MULTIPLE COLLINEARITY AND ERRORS-IN-VARIABLES 40
3.3.1 MULTIPLE COLLINEARITY 41
3.3.2 ERRORS-IN-VARIABLES. THE STRUCTURAL MODEL AND INSTRUMENTAL
VARIABLE ESTIMATION 42
3.4 CONNECTION WITH STOCHASTIC APPROXIMATION 45
3.5 EXERCISES 45
3.6 SUMMARY 45
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011959259
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
4 RECURSIVE ESTIMATION OF TIME VARIABLE PARAMETERS IN REGRESSION MODELS
47
4.1 SHAPING THE MEMORY OF THE ESTIMATOR 50
4.1.1 THE MOVING RECTANGULAR WINDOW (RW) 50
4.1.2 THE MOVING EXPONENTIALLY-WEIGHTED-PAST (EWP) WINDOW 53
4.2 MODELLING THE PARAMETER VARIATIONS 59
4.2.1 THE COMPLETE TVP REGRESSION MODEL 67
4.3 VECTOR MEASUREMENTS 69
4.4 THE KAIMAN FILTER 71
4.5 RECURSIVE FIXED-INTERVAL SMOOTHING 76
4.5.1 SIMPLE FIS ESTIMATION 77
4.5.2 OPTIMAL FIS ALGORITHMS 78
4.5.3 OPTIMIZATION OF HYPER-PARAMETERS 81
4.5.4 IMPLEMENTATION OF THE KALMSMO ALGORITHM 82 4.5.5 THE PHYSICAL
NATURE OF FIS ESTIMATION 85
4.6 FINAL RECURSIVE ANALYSIS OF THE WALGETT DATA 86
4.6.1 STATISTICAL METHODS FOR DETECTING THE PRESENCE OF PARAMETER
VARIATION 88
4.7 SIMPLIFIED CONSTANT GAIN ALGORITHMS FOR TIME VARIABLE PARAMETER
ESTIMATION 92
4.8 THE ESTIMATION OF RAPIDLY VARYING PARAMETERS 94
4.9 VARIANCE INTERVENTION 96
4.10 EXERCISES 97
4.11 SUMMARY 98
5 UNOBSERVED COMPONENT MODELS 99
5.1 THE DYNAMIC LINEAR REGRESSION (DLR) MODEL 102
5.1.1 EXAMPLE: DLR ANALYSIS OF LIDAR DATA 103
5.2 THE DYNAMIC HARMONIC REGRESSION (DHR) MODEL AND TIME SERIES
FORECASTING 106
5.2.1 SPECTRAL ANALYSIS OF THE DHR MODEL 109
5.2.2 THE COMPLETE DHR ESTIMATION ALGORITHM 114
5.2.3 PRACTICAL EXAMPLE: SIGNALS PASSED AT DANGER (SPAD) DATA 115
5.2.4 EXTENSIONS OF DHR MODEL ANALYSIS 121
5.3 THE DYNAMIC AUTOREGRESSION (DAR) MODEL AND TIME- FREQUENCY ANALYSIS
121
5.3.1 PRACTICAL EXAMPLE: PALAEOCLIMATIC DATA ANALYSIS 122 5.4 DYNAMIC
ARX AND FIR MODELS 128
5.4.1 EXAMPLE: DARX MODEL ESTIMATION 131
5.5 FORECASTING WITH UC MODELS 134
5.6 EXERCISES 136
5.7 SUMMARY 136
IMAGE 3
CONTENTS XIII
PART II RECURSIVE ESTIMATION OF PARAMETERS IN TRANSFER FUNCTION MODELS
6 TRANSFER FUNCTION MODELS AND THE LIMITATIONS OF RECURSIVE LEAST
SQUARES 139
6.1 INTRODUCTION: DIRECT ESTIMATION OF THE STATE SPACE MODEL 140 6.2
FROM STATE SPACE TO OBSERVATION SPACE 141
6.3 LEAST SQUARES ESTIMATION: ITS ADVANTAGES AND LIMITATIONS 150 6.4
LEAST SQUARES ESTIMATION: ARX MODEL ESTIMATION 154 6.4.1 EXAMPLE 6.1 :
ESTIMATION OF A SIMPLE ARX MODEL 155 6.5 LEAST SQUARES ESTIMATION: FIR
MODEL ESTIMATION 162
6.5.1 EXAMPLE 6.2: ESTIMATION OF A SIMPLE FIR MODEL 163 6.6
IDENTIFIABILITY 164
6.6.1 CHOICE OF INPUT SIGNALS 166
6.6.2 RESTRICTIONS ON THE SYSTEM TO BE IDENTIFIED 168
6.6.3 THE MORE GENERAL CASE 168
6.6.4 NOISE PROCESS IDENTIFIABILITY 169
6.6.5 SOME CONCLUDING COMMENTS ON IDENTIFIABILITY 169 6.7 RECURSIVE
ESTIMATION OF TRANSFER FUNCTION MODELS 170 6.8 STANDARD INSTRUMENTAL
VARIABLE (SIV) ESTIMATION 171
6.8.1 STATISTICAL PROPERTIES OF SIV ESTIMATES 174
6.9 MODEL STRUCTURE IDENTIFICATION 176
6.9.1 EXAMPLE 6.3: RECURSIVE SIV PARAMETER ESTIMATION FOR A SIMPLE TF
MODEL 179
6.9.2 EXAMPLE 6.4: SIV ESTIMATION OF TRACER EXPERIMENT DATA 181 6.10
DYNAMIC TRANSFER FUNCTION MODELS 185
6.10.1 EXAMPLE 6.5: DTF MODEL ESTIMATION 188
6.10.2 EXAMPLE: USING DTF ESTIMATION FOR MODEL DIAGNOSIS 189 6.11
MULTIVARIABLE TRANSFER FUNCTION MODELS 192
6.12 EXERCISES 194
6.13 SUMMARY 195
7 OPTIMAL IDENTIFICATION AND ESTIMATION OF DISCRETE-TIME TRANSFER
FUNCTION MODELS 197
7.1 REFINED INSTRUMENTAL VARIABLE ESTIMATION 200
7.1.1 RECURSIVE-ITERATIVE INSTRUMENTAL VARIABLE ESTIMATION 200 7.1.2 THE
SYSTEM TF ESTIMATION MODEL AND RIV ESTIMATION 202 7.1.3 THE ARMA NOISE
ESTIMATION MODEL AND IVARMA ESTIMATION 204
7.2 THE RECURSIVE-ITERATIVE ALGORITHMS 207
7.2.1 IMPLEMENTATION OF THE RIV AND SRIV ALGORITHMS 208 7.2.2
CONVERGENCE OF THE ITERATIVE ALGORITHMS 209
7.2.3 THEORETICAL JUSTIFICATION OF THE RIV METHOD 210
7.3 MODEL STRUCTURE IDENTIFICATION 212
7.4 INPUT NOISE AND ERRORS-IN-VARIABLES 213
7.4.1 EXAMPLE 7.1: ERRORS-IN-VARIABLES: THE EFFECTS OF INPUT NOISE 216
IMAGE 4
CONTENTS
7.5 EXAMPLES OF RIV IDENTIFICATION AND ESTIMATION: SISO MODELS 220 7.5.1
EXAMPLE 7.2: DISCRETE-TIME SIMULATION EXAMPLE 1 220 7.5.2 EXAMPLE 7.3:
DISCRETE-TIME SIMULATION EXAMPLE 2 222 7.5.3 EXAMPLE 7.4: EVALUATING
OVER-PARAMETERIZATION 224 7.5.4 EXAMPLE 7.5: RIV ESTIMATION OF TRACER
EXPERIMENT DATA . . . . 2 25
7.6 MISO MODEL ESTIMATION 227
7.7 EXAMPLES OF SRIVDD IDENTIFICATION AND ESTIMATION FOR MISO MODELS 231
7.7.1 EXAMPLE 7.6: SIMULATION RESULTS FOR A 3-INPUT MISO MODEL 231
7.7.2 EXAMPLE 7.7: SRIVDD MODELLING OF A MISO WINDING PROCESS 233
7.7.3 EXAMPLE 7.8: SRIVDD EVALUATION: MONTE CARLO SIMULATION RESULTS 236
7.8 OPTIMAL PREFILTERS AND AN ADAPTIVE KAIMAN FILTER 237
7.9 EXERCISES 238
7.10 SUMMARY 239
OPTIMAL IDENTIFICATION AND ESTIMATION OF CONTINUOUS-TIME TRANSFER
FUNCTION MODELS 241
8.1 INTRODUCTION 241
8.2 TF CONVERSION BETWEEN CONTINUOUS AND DISCRETE-TIME 243 8.3 HYBRID
CONTINUOUS-TIME RIVC ESTIMATION 244
8.4 THE ITERATIVE RIVC AND SRIVC ALGORITHMS 248
8.5 MODEL STRUCTURE IDENTIFICATION AND MISO MODEL ESTIMATION 250 8.6
EXAMPLES OF RIVC IDENTIFICATION AND ESTIMATION 251
8.6.1 EXAMPLE 7.1 : CONTINUOUS-TIME SIMULATION EXAMPLE 251 8.6.2 EXAMPLE
7.2: RIVC SISO ESTIMATION OF TRACER EXPERIMENT DATA 254
8.6.3 EXAMPLE 7.3: SRIVCDD MISO MODELLING OF THE TRACER EXPERIMENT DATA
256
8.6.4 EXAMPLE 7.4: EVALUATION OF A GLOBAL CIRCULATION M O D E L . . ..
261 8.7 SAMPLING CONSIDERATIONS 264
8.7.1 THE EFFECTS OF SAMPLING INTERVAL ON ESTIMATION ACCURACY . . .. 265
8.8 EXERCISES 268
8.9 SUMMARY AND CONCLUSIONS 269
IDENTIFICATION OF TRANSFER FUNCTION MODELS IN CLOSED-LOOP 271 9.1
INTRODUCTION 271
9.2 THE GENERALIZED BOX-JENKINS MODEL IN A CLOSED-LOOP CONTEXT 272 9.3
CLOSED-LOOP IDENTIFICATION AND ESTIMATION 274
9.3.1 SIMPLE CLSRIV AND CLSRIVC TWO-STAGE CLOSED- LOOP ESTIMATION 274
9.3.2 THREE-STAGE CLRIV AND CLRIVC CLOSED-LOOP ESTIMATION... 275 9.3.3
UNSTABLE SYSTEMS 276
IMAGE 5
CONTENTS XV
9.4 SIMULATION EXAMPLES 277
9.4.1 EXAMPLE 9.1: CLOSED-LOOP, STABLE, DISCRETE-TIME SYSTEM ESTIMATION
278
9.4.2 EXAMPLE 9.2: CLOSED-LOOP, STABLE, CONTINUOUS-TIME SYSTEM
ESTIMATION 280
9.4.3 EXAMPLE 9.3: CLOSED-LOOP, UNSTABLE AND MARGINALLY STABLE SYSTEM
ESTIMATION 283
9.5 EXERCISES 286
9.6 SUMMARY AND CONCLUSIONS 287
10 REAL-TIME RECURSIVE PARAMETER ESTIMATION 289
10. 1 PREDICTION ERROR (PE) METHODS AND THE RPEM ALGORITHM 290 10.1.1
STATISTICAL PROPERTIES OF THE PEM ESTIMATES FOR THE BJ MODEL 295
10.2 REAL-TIME RECURSIVE RRIV ESTIMATION 297
10.2.1 THE RECURSIVE ALGORITHMS 297
10.2.2 IMPLEMENTATION 299
10.2.3 EXAMPLE 10.1: RSRIV ESTIMATION OF TVPS IN A SIMULATED 2 ND ORDER
TF MODEL 301
10.3 THE EXTENDED KAIMAN FILTER 304
10.3.1 THE EKF IN A RECURSIVE PREDICTION ERROR FORM 310 10.4
COMPUTATIONALLY INTENSIVE METHODS OF RECURSIVE ESTIMATION 311 10.5
EXAMPLE 12.1: DATA ASSIMILATION AND ADAPTIVE FORECASTING 315
10.5.1 THE DBM MODEL 316
10.5.2 PARAMETER UPDATING BY RRIV ESTIMATION 319
10.5.3 STATE UPDATING BY THE KAIMAN FILTER 320
10.5.4 TYPICAL ADAPTIVE FORECASTING RESULTS 320
10.6 EXERCISES 322
10.7 SUMMARY 323
PART III OTHER TOPICS
11 STATE-DEPENDENT PARAMETER (SDP) ESTIMATION 327
11.1 INTRODUCTION 327
11.2 SDP IDENTIFICATION OF NONLINEAR INPUT-OUTPUT SYSTEMS 329 11.2.1
FULL SDP ESTIMATION 331
11.2.2 PARAMETERIZATION AND FINAL NONLINEAR MODEL ESTIMATION 335 11.2.3
THE PROBLEM OF ERRORS-IN-VARIABLES (EIV) ESTIMATION 338 .3 SDP
IDENTIFICATION OF PURELY STOCHASTIC NONLINEAR SYSTEMS 345 .4 SDP
ESTIMATION IN HYDROLOGY 352
.5 SDP ESTIMATION IN FORECASTING AND AUTOMATIC CONTROL 352 .6 EXERCISES
353
.7 SUMMARY AND CONCLUSIONS 354
IMAGE 6
CONTENTS
12 DATA-BASED MECHANISTIC (DBM) MODELLING 357
12.1 INTRODUCTION 357
12.2 A BRIEF REVIEW OF DATA-BASED MECHANISTIC MODELLING 359 12.3 MODEL
ORDER REDUCTION 362
12.3.1 THE ALSTOM GASIFIER EXAMPLE 363
12.4 LARGE COMPUTER MODEL EMULATION 365
12.5 AN ILLUSTRATIVE EXAMPLE: DBM MODELLING OF POLLUTION TRANSPORT IN A
WETLAND AREA 367
12.5.1 THE LARGE SIMULATION MODEL 368
12.5.2 EMULATION MODELLING 372
12.5.3 MODELLING FROM REAL DATA 375
12.6 EXERCISES 380
12.7 CONCLUSIONS 380
EPILOGUE 382
A THE K. F. GAUSS DERIVATION OF RECURSIVE LEAST SQUARES
B BASIC MATHEMATICAL AND STATISTICAL BACKGROUND
389
397
B.I MATRIX ALGEBRA 397
B. 1.1 MATRICES 397
B.1.2 VECTORS 398
B.I.3 MATRIX ADDITION (OR SUBTRACTION) 398
B. 1.4 MATRIX OR VECTOR TRANSPOSE 398
B.1.5 MATRIX MULTIPLICATION 399
B. 1.6 DETERMINANT OF A MATRIX 400
B. 1.7 PARTITIONED MATRICES 401
B. 1.8 INVERSE OF A MATRIX 402
B. 1.9 QUADRATIC FORMS 403
B. 1.10 POSITIVE DEFINITE OR SEMI-DEFINITE MATRICES 403 B. 1.11 THE RANK
OF A MATRIX 403
B. 1.12 DIFFERENTIATION OF VECTORS AND MATRICES 403
B. 1.13 CHOLESKY DECOMPOSITION 405
B. 1.14 SINGULAR VALUE DECOMPOSITION (SVD) 406
B.2 STATISTICS AND PROBABILITY 407
B.2.1 DISCRETE RANDOM VARIABLES 407
B.2.2 LAW OF LARGE NUMBERS 408
B.2.3 DISCRETE RANDOM VECTORS 408
B.2.4 CONDITIONAL PROBABILITIES 409
B.2.5 CONTINUOUS RANDOM VARIABLES AND VECTORS 410
B.2.6 THE NORMAL OR GAUSSIAN DENSITY FUNCTION 410
B.2.7 PROPERTIES OF ESTIMATORS 411
B.2.8 THE LIKELIHOOD FUNCTION AND MAXIMUM LIKELIHOOD ESTIMATION 412
IMAGE 7
CONTENTS XVII
B.2.9 THE CRAMER-RAO LOWER BOUND 414
B.2.10 MAXIMUM LIKELIHOOD ESTIMATORS: THE VECTOR CASE 414 B.3 TIME
SERIES 415
B.3.1 GAUSS-MARKOV RANDOM PROCESSES 417
B.3.2 THE STATE SPACE MODEL OF A LINEAR, DISCRETE-TIME, STOCHASTIC
DYNAMIC SYSTEM 418
B.3.3 THE DISCRETE-TIME TRANSFER FUNCTION MODEL 419 B.3.4
CONTINUOUS-TIME, STOCHASTIC DYNAMIC MODELS 423 B.3.5 HYBRID STOCHASTIC
DYNAMIC MODELS 424
B.3.6 MULTIVARIABLE (MULTI-INPUT, MULTI-OUTPUT) TF MODELS 426 B.3.7
PHYSICAL INTERPRETATION OF TF MODELS 427
B.3.8 DIFFERENTIATION OF A TF WITH RESPECT TO A GIVEN PARAMETER 439
B.3.9 A SIMPLE INTRODUCTION TO MONTE CARLO SIMULATION 439
C STOCHASTIC APPROXIMATION 445
C. 1 SOME EXTENSIONS TO STOCHASTIC APPROXIMATION 451
C. 1.1 MATRIX GAIN SA AND OPTIMUM ALGORITHMS 451
C. 1.2 CONTINUOUS-TIME ALGORITHMS 452
C. 1.3 SEARCH ALGORITHMS 453
C. 1.4 ACCELERATION OF CONVERGENCE 453
C.2 SUMMARY 454
D DETERMINISTIC REGULARIZATION AND STOCHASTIC FIXED INTERVAL SMOOTHING
455
D. 1 WIENER-KOLMOGOROV-WHITTLE OPTIMAL SIGNAL EXTRACTION 457
E THE INSTANTANEOUS COST FUNCTION ASSOCIATED WITH THE RECURSIVE LEAST
SQUARES ALGORITHM 461
F MAXIMUM LIKELIHOOD DERIVATION OF THE REFINED INSTRUMENTAL VARIABLE
ALGORITHM 465
F.I RIV SYSTEM MODEL ESTIMATION WITHIN THE CONTEXT OF MAXIMUM LIKELIHOOD
467
G THE CAPTAIN TOOLBOX FOR MATLAB: AN OVERVIEW 469
GLOSSARY 473
REFERENCES 477
INDEX 499
|
| any_adam_object | 1 |
| author | Young, Peter C. 1939- |
| author_GND | (DE-588)170667308 |
| author_facet | Young, Peter C. 1939- |
| author_role | aut |
| author_sort | Young, Peter C. 1939- |
| author_variant | p c y pc pcy |
| building | Verbundindex |
| bvnumber | BV039672695 |
| classification_rvk | SK 845 |
| ctrlnum | (OCoLC)777147912 (DE-599)DNB1011959259 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV039672695 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T15:59:53Z |
| institution | BVB |
| isbn | 3642219802 9783642219801 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024521805 |
| oclc_num | 777147912 |
| open_access_boolean | |
| owner | DE-11 DE-83 DE-824 DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-83 DE-824 DE-19 DE-BY-UBM |
| physical | XVII, 504 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Young, Peter C. 1939- Recursive estimation and time-series analysis an introduction for the student and practitioner Zeitreihenanalyse (DE-588)4067486-1 gnd Rekursive Parameterschätzung (DE-588)4199569-7 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4199569-7 |
| title | Recursive estimation and time-series analysis an introduction for the student and practitioner |
| title_auth | Recursive estimation and time-series analysis an introduction for the student and practitioner |
| title_exact_search | Recursive estimation and time-series analysis an introduction for the student and practitioner |
| title_full | Recursive estimation and time-series analysis an introduction for the student and practitioner Peter C. Young |
| title_fullStr | Recursive estimation and time-series analysis an introduction for the student and practitioner Peter C. Young |
| title_full_unstemmed | Recursive estimation and time-series analysis an introduction for the student and practitioner Peter C. Young |
| title_short | Recursive estimation and time-series analysis |
| title_sort | recursive estimation and time series analysis an introduction for the student and practitioner |
| title_sub | an introduction for the student and practitioner |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Rekursive Parameterschätzung (DE-588)4199569-7 gnd |
| topic_facet | Zeitreihenanalyse Rekursive Parameterschätzung |
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| work_keys_str_mv | AT youngpeterc recursiveestimationandtimeseriesanalysisanintroductionforthestudentandpractitioner |