Time Series Modelling of Water Resources and Environmental Systems

Hipel, Keith W.; McLeod, A. Ian.0-444-89270-2

Table of contents :
Time Series Modelling of Water Resources and Environmental Systems……Page 4
Copyright Page……Page 5
TABLE OF CONTENTS……Page 8
PART I: SCOPE AND BACKGROUND MATERIAL……Page 40
1.1. THE NEW FIELD OF ENVIRONMETRICS……Page 42
1.2. THE SCIENTIFIC METHOD……Page 45
1.3. PHILOSOPHY OF MODEL BUILDING……Page 55
1.4. THE HYDROLOGICAL CYCLE……Page 58
1.5. DECISION MAKING……Page 63
1.6. ORGANIZATION OF THE BOOK……Page 74
1.7. DECISION SUPPORT SYSTEM FOR TIME SERIES MODELLING……Page 90
1.8. CONCLUDING REMARKS……Page 91
PROBLEMS……Page 93
REFERENCES……Page 94
2.2. TIME SERIES……Page 102
2.3. STOCHASTIC PROCESS……Page 104
2.4. STATIONARITY……Page 106
2.5. STATISTICAL DEFINITIONS……Page 108
2.6. SPECTRAL ANALYSIS……Page 116
2.7. LINEAR STOCHASTIC MODELS……Page 118
PROBLEMS……Page 122
REFERENCES……Page 123
PART II: LINEAR NONSEASONAL MODELS……Page 126
3.1. INTRODUCI’ION……Page 130
3.2. AUTOREGRESSIVE PROCESSES……Page 131
3.3. MOVING AVERAGE PROCESSES……Page 141
3.4. AUTOREGRESSIVE – MOVING AVERAGE PROCESSES……Page 146
3.5. THEORETlCAL SPECTRUM……Page 162
3.6. PHYSICAL JUSTIFICATION OF ARMA MODELS……Page 171
3.7. CONCLUSIONS……Page 175
APPENDIX A3.1. – ALGORITHM FOR ESTIMATING THE PARTIAL AUTOCORRELATION FUNCTION……Page 176
APPENDIX A3.2. – THEORETlCAL ACF FOR AN ARMA PROCESS
……Page 178
PROBLEMS……Page 179
REFERENCES……Page 181
4.2. EXPLOSIVE NONSTATIONARITY……Page 184
4.3. HOMOGENEOUS NONSTATIONARITY……Page 185
4.4. INTEGRATED MOVING AVERAGE PROCESSES……Page 202
4.5. DIFFERENCING ANALOGIES……Page 204
4.6. DETERMINISTIC AND STOCHASTlC TRENDS……Page 206
PROBLEMS……Page 207
REFERENES……Page 208
PART III: MODEL CONSTRUCTION……Page 210
5.2. MODELLING PHILOSOPHIES……Page 212
5.3. IDENTIFICATION METHODS……Page 214
5.4. APPLICATIONS……Page 224
5.5. OTHER IDENTIFICATION METHODS……Page 233
5.6. CONCLUSIONS……Page 234
PROBLEMS……Page 235
REFERENCES……Page 236
6.1. INTRODUCTION……Page 242
6.2. MAXIMUM LIKELIHOOD ESTIMATION……Page 243
6.3. MODEL DISCRIMINATION USING THE AKAIKE INFORMATION CRITERION……Page 249
6.4. APPLICATIONS……Page 255
APPENDIX A6.1. – ESTIMATOR FOR ARMA MODELS……Page 260
APPENDIX A6.2. – INFORMATION MATRIX
……Page 264
APPENDIX A6.3. – FINAL PREDICTION ERROR……Page 266
PROBLEMS……Page 267
REFERENCES……Page 268
7.1. INTRODUCTION……Page 274
7.2. OVERFITTING……Page 275
7.3. WHITENESS TESTS……Page 277
7.4. NORMALITY TESTS……Page 280
7.5. CONSTANT VARIANCE TESTS……Page 284
7.6. APPLICATIONS……Page 285
7.7. CONCLUSIONS……Page 288
PROBLEMS……Page 289
REFERENCES……Page 291
PART IV: FORECASTING AND SIMULATION……Page 294
8.1. INTRODUCTION……Page 296
8.2. MINIMUM MEAN SQUARE ERROR FORECASTS……Page 298
8.3. FORECASTING EXPERlMENTS……Page 312
8.4. CONCLUSIONS……Page 323
PROBLEMS……Page 326
REFERENCES……Page 327
9.1. INTRODUCTION……Page 332
9.2. GENERATING WHITE NOISE……Page 334
9.3. WATERLOO SIMULATION PROCEDURE 1……Page 343
9.4. WATERLOO SIMULATION PROCEDURE 2……Page 345
9.5. SIMULATION OF INTEGRATED MODELS……Page 349
9.6. INVERSE BOX-COX TRANSFORMATION……Page 351
9.7. WATERLOO SIMULATION PROCEDURE 3……Page 352
9.8. APPLICATIONS……Page 355
9.9. CONCLUSIONS……Page 358
PROBLEMS……Page 359
REFERENCES……Page 360
PART V: LONG MEMORY MODELLING……Page 364
10.1. INTRODUCTION……Page 366
10.2. DEFINITIONS……Page 367
10.3. HISTORICAL RESEARCH……Page 370
10.4. FRACTIONAL GAUSSIAN NOISE……Page 377
10.5. SIMULATION STUDIES……Page 391
10.6. PRESERVATION OF THE RESCALED ADJUSTED RANGE……Page 401
10.7. ESTIMATES OF THE HURST COEFFICIENT……Page 408
10.8. CONCLUSIONS……Page 410
APPENDIX A10.1. – REPRESENTATIVE EMPIRICAL CUMULATIVE DISTRIBUTION FUNCTIONS (ECDF‘S) FOR HURST STATISTICS……Page 413
PROBLEMS……Page 420
REFERENCES……Page 421
11.1. INTRODUCTION……Page 428
11.2. DEFINITIONS AND STATISTICAL PROPERTIES……Page 429
11.3. CONSTRUCTING FARMA MODELS……Page 436
11.4. SIMULATION AND FORECASTING……Page 439
11.5. FITTING FARMA MODELS TO ANNUAL HYDROLOGICAL TIME SERIES……Page 442
11.6. CONCLUSIONS……Page 446
APPENDIX A 11.1. – ESTIMATION ALGORITHM FOR FARMA MODELS……Page 448
PROBLEMS……Page 450
REFERENCES……Page 451
PART VI: SEASONAL MODELS……Page 454
12.1. INTRODUCTION……Page 458
12.2. MODEL DESIGN……Page 459
12.3. MODEL CONSTRUCTION……Page 466
12.4. APPLICATIONS……Page 477
12.6. CONCLUSIONS……Page 490
APPENDIX A12.1. – DESIGNING MULTIPLICATIVE SARIMA MODELS USING THE ACF……Page 492
APPENDIX A12.2. – MAXIMUM LIKELIHOOD ESTIMATION FOR SARMA MODELS……Page 494
PROBLEMS……Page 498
REFERENCES……Page 499
13.1. INTRODUCTION……Page 502
13.2. DEFINITIONS OF DESEASONALIZED MODELS……Page 503
13.3. CONSTRUCTING DESEASONALIED MODELS……Page 506
13.4. APPLICATIONS OF DESEASONALIZED MODELS……Page 512
13.5. FORECASTING AND SIMULATING WITH DESEASONALJZED MODELS……Page 517
13.6. CONCLUSIONS……Page 518
PROBLEMS……Page 519
REFERENCES……Page 520
14.1. INTRODUCTION……Page 522
14.2. DEFINITIONS OF PERIODIC MODELS……Page 523
14.3. CONSTRUCTING PAR MODELS……Page 532
14.4. PAR MODELLING APPLICATION……Page 540
14.5. PARSIMONIOUS PERIODIC AUTOREGRESSIVE (PPAR) MODELS……Page 542
14.6. APPLICATIONS OF SEASONAL MODELS……Page 546
14.7. CONSTRUCTING PARMA MODELS……Page 549
14.8. SIMULATING AND FORECASTING WITH PERIODIC MODELS……Page 551
14.9. CONCLUSIONS……Page 556
PROBLEMS……Page 557
REFERENCES……Page 559
15.1. INTRODUCTION……Page 564
15.2. CALCULATING FORECASTS FOR SEASONAL MODELS……Page 565
15.3. FORECASTING MONTHLY RIVERFLOW TIME SERIES……Page 571
15.4. FORECASTING QUARTER MONTHLY AND MONTHLY RIVERFLOWS……Page 579
15.5. COMBINING FORECASTS ACROSS MODELS……Page 583
PROBLEMS……Page 586
REFERENCES……Page 588
PART VII: MULTIPLE INPUT – SINGLE OUTPUT MODELS……Page 592
16.1. INTRODUCTION……Page 594
16.2. CAUSALITY……Page 595
16.3. APPLICATIONS……Page 600
16.4. CONCLUSIONS……Page 605
PROBLEMS……Page 608
REFERENCES……Page 609
17.1. INTRODUCTION……Page 612
17.2. TRANSFER FUNCTION-NOISE MODELS WITH A SINGLE INPUT……Page 613
17.3. MODEL CONSTRUCTION FOR TRANSFER FUNCTION-NOISE MODELS……Page 619
17.4. HYDROLOGICAL APPLICATIONS OF TRANSFER FUNCTION-NOISE MODELS WITH A SINGLE INPUT……Page 627
17.5. TRANSFER FUNCTION-NOISE MODELS WITH MULTIPLE INPUTS……Page 632
17.6. ARMAX MODELS……Page 644
17.7. CONCLUSIONS……Page 647
APPENDIX A 17.1. – ESTIMATOR FOR TFN MODELS
……Page 648
PROBLEMS……Page 651
REFERENCES……Page 653
18.1. INTRODUCTION……Page 656
18.2. FORECASTING PROCEDURES FOR TFN MODELS……Page 657
18.3. FORECASTING QUARTER-MONTHLY RIVERFLOWS……Page 668
18.4. COMBINING HYDROLOGICAL FORECASTS……Page 680
18.5. RECORD EXTENSIONS, CONTROL AND SIMULATION……Page 683
18.6. CONCLUSIONS……Page 686
PROBLEMS……Page 687
REFERENCES……Page 689
PART VIII: INTERVENTION ANALYSIS……Page 692
19.1. INTRODUCTION……Page 694
19.2. INTERVENTION MODELS WITH MULTIPLE INTERVENTIONS……Page 699
19.3. DATA FILLING USING INTERVENTION ANALYSIS……Page 732
19.4. INTERVENTION MODELS WITH MULTIPLE INTERVENTIONS ANDMISSING OBSERVATIONS……Page 741
19.5. INTERVENTION MODELS WITH MULTIPLE INTERVENTIONS, MISSING OBSERVATIONS AND INPUT SERIES……Page 748
19.6. PERIODIC INTERVENTION MODELS……Page 762
19.7. DATA COLLECTION……Page 765
19.8. CONCLUSIONS……Page 766
PROBLEMS……Page 769
REFERENCES……Page 772
PART IX: MULTIPLE INPUT-MULTIPLE OUTPUT MODELS……Page 778
20.1. INTRODUCTION……Page 780
20.2. DEFINITIONS OF MULTIVARIATE ARMA MODELS……Page 782
20.3. CONSTRUCTING GENERAL MULTIVARIATE ARMA MODELS……Page 786
20.4. HISTORICAL DEVELOPMENT……Page 791
20.5. OTHER FAMILIES OF MULTIVARIATE MODELS……Page 794
20.6. CONCLUSIONS……Page 798
APPENDIX A20.1. – IDENTIFICATION METHODS FOR GENERAL MULTIVARIATE ARMA MODELS
……Page 800
PROBLEMS……Page 806
REFERENCES……Page 808
21.1. INTRODUCTION……Page 818
21.2. DERIVING CARMA MODELS……Page 819
21.3. CONSTRUCTING CARMA MODELS……Page 823
21.4. SIMULATING USING CARMA MODELS……Page 829
21.5. PRAClTCAL APPLICATIONS……Page 831
21.6. CONCLUSIONS……Page 837
APPENDIX A21.1. – ESTIMATOR FOR CARMA MODELS HAVING UNEQUAL SAMPLE SIZES
……Page 839
PROBLEMS……Page 841
REFERENCES……Page 843
PART X: HANDLING MESSY ENVIRONMENTAL DATA……Page 846
22.1. INTRODUCTION……Page 848
22.2. DATA FILLING USING SEASONAL ADJUSTMENT……Page 850
22.3. EXPLORATORY DATA ANALYSIS……Page 852
22.4. CONFIRMATORY DATA ANALYSIS USING INTERVENTION ANALYSIS……Page 876
22.5. CONCLUSIONS……Page 886
PROBLEMS……Page 887
REFERENCES……Page 889
23.1. INTRODUCTION……Page 892
23.2. STATISTICAL TESTS……Page 897
23.3. NONPARAMETRIC TESTS……Page 900
23.4. POWER COMPARISONS OF PARAMETIC AND NONPARAMETRIC TREND TESTS……Page 930
23.5. WATER QUALITY APPLICATIONS……Page 941
23.6. CONCLUSIONS……Page 961
APPENDIX A23.1. – KENDALL RANK CORRELATION TEST……Page 963
APPENDIX A23.2. – WILCOXON SIGNED RANK TEST
……Page 964
APPENDIX A23.3. – KRUSKAL-WALLIS TEST……Page 966
PROBLEMS……Page 967
REFERENCES……Page 969
24.1. INTRODUCTION……Page 978
24.2. REGRESSION ANALYSIS……Page 979
24.3. TREND ANALYSIS METHODOLOGY FOR WATER QUALITY TIME SERIES……Page 995
24.4. CONCLUSIONS……Page 1009
PROBLEMS……Page 1011
REFERENCES……Page 1013
DATA ACQUISITION……Page 1018
DATA LISTING……Page 1019
REFERENCES……Page 1026
AUTHOR INDEX……Page 1028
SUBJECT INDEX……Page 1040