Introduction to time series and forecasting: [includes ITSM 2000]
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2002
|
| Edition: | 2. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 434 S. graph. Darst. CD-ROM (12 cm) |
| Format: | Systemvoraussetzungen der CD-ROM-Beil.: IBM PC or equivalent; 5 MB of hard disk space;. - Windows 95, NT 4.0 or later versions |
| ISBN: | 9780387953519 0387953515 |
Staff View
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| 245 | 1 | 0 | |a Introduction to time series and forecasting |b [includes ITSM 2000] |c Peter J. Brockwell ; Richard A. Davis |
| 250 | |a 2. ed. | ||
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Record in the Search Index
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| adam_text |
PETER J. BROCKWELL RICHARD A. DAVIS INTRODUCTION TO TIME SERIES AND
FORECASTING SECOND EDITION WITH 126 ILLUSTRATIONS INCLUDES CD-ROM
SPRINGER CONTENTS PREFACE VII 1. INTRODUCTION 1 1.1. EXAMPLES OF TIME
SERIES 1 1.2. OBJECTIVES OF TIME SERIES ANALYSIS 6 1.3. SOME SIMPLE TIME
SERIES MODELS 7 1.3.1. SOME ZERO-MEAN MODELS 8 1.3.2. MODELS WITH TREND
AND SEASONALITY 9 1.3.3. A GENERAL APPROACH TO TIME SERIES MODELING 14
1.4. STATIONARY MODELS AND THE AUTOCORRELATION FUNCTION : 15 1.4.1. THE
SAMPLE AUTOCORRELATION FUNCTION 18 1.4.2. A MODEL FOR THE LAKE HURON
DATA 21 1.5. ESTIMATION AND ELIMINATION OF TREND AND SEASONAL COMPONENTS
23 1.5.1. ESTIMATION AND ELIMINATION OF TREND IN THE ABSENCE OF
SEASONALITY 24 1.5.2. ESTIMATION AND ELIMINATION OF BOTH TREND AND
SEASONALITY 31 1.6. TESTING THE ESTIMATED NOISE SEQUENCE 35 PROBLEMS 40
2. STATIONARY PROCESSES 45 2.1. BASIC PROPERTIES 45 2.2. LINEAR
PROCESSES 51 2.3. INTRODUCTION TO ARMA PROCESSES 55 2.4. PROPERTIES OF
THE SAMPLE MEAN AND AUTOCORRELATION FUNCTION 57 2.4.1. ESTIMATION OF /X
58 2.4.2. ESTIMATION OF Y (*) AND P(-) 59 2.5. FORECASTING STATIONARY
TIME SERIES 63 2.5.1. THE DURBIN-LEVINSON ALGORITHM 69 2.5.2. THE
INNOVATIONS ALGORITHM 71 2.5.3. PREDICTION OF A STATIONARY PROCESS IN
TERMS OF INFINITELY MANY PAST VALUES 75 CONTENTS 2.6. THE WOLD
DECOMPOSITION 77 PROBLEMS 78 3. ARMA MODELS 83 3.1. ARMA(P, Q) PROCESSES
83 3.2. THEACFANDPACFOFANARMA(P,?)PROCESS 88 3.2.1. CALCULATION OF THE
ACVF 88 3.2.2. THE AUTOCORRELATION FUNCTION 94 3.2.3. THE PARTIAL
AUTOCORRELATION FUNCTION 94 3.2.4. EXAMPLES 96 3.3. FORECASTING ARMA
PROCESSES 100 PROBLEMS 108 4. SPECTRAL ANALYSIS 111 4.1. SPECTRAL
DENSITIES 112 4.2. THE PERIODOGRAM 121 4.3. TIME-INVARIANT LINEAR
FILTERS 127 4.4. THE SPECTRAL DENSITY OF AN ARMA PROCESS 132 PROBLEMS
134 5. MODELING AND FORECASTING WITH ARMA PROCESSES 137 5.1. PRELIMINARY
ESTIMATION 138 5.1.1. YULE-WALKER ESTIMATION 139 5.1.2. BURG'S ALGORITHM
147 5.1.3. THE INNOVATIONS ALGORITHM 150 5.1.4. THE HANNAN-RISSANEN
ALGORITHM 156 5.2. MAXIMUM LIKELIHOOD ESTIMATION 158 5.3. DIAGNOSTIC
CHECKING 164 5.3.1. THE GRAPH OF {K T , T = 1,., N) 165 5.3.2. THE
SAMPLE ACF OF THE RESIDUAIS 166 5.3.3. TESTS FOR RANDOMNESS OF THE
RESIDUAIS 166 5.4. FORECASTING 167 5.5. ORDER SELECTION 169 5.5.1. THE
FPECRITERION 170 5.5.2. THE AICC CRITERION 171 PROBLEMS 174 6.
NONSTATIONARY AND SEASONAL TIME SERIES MODELS 179 6.1. ARIMA MODELS FOR
NONSTATIONARY TIME SERIES 180 6.2. IDENTIFICATION TECHNIQUES 187
CONTENTS 6.3. UNIT ROOTS IN TIME SERIES MODELS 193 6.3.1. UNIT ROOTS IN
AUTOREGRESSIONS 194 6.3.2. UNIT ROOTS IN MOVING AVERAGES 196 6.4.
FORECASTING ARIMA MODELS 198 6.4.1. THE FORECAST FUNCTION 200 6.5.
SEASONAL ARIMA MODELS 203 6.5.1. FORECASTING SARIMA PROCESSES 208 6.6.
REGRESSION WITH ARMA ERRORS 210 6.6.1. OLS AND GLS ESTIMATION 210 6.6.2.
ML ESTIMATION 213 PROBLEMS 219 7. MULTIVARIATE TIME SERIES 223 7.1.
EXAMPLES 224 7.2. SECOND-ORDER PROPERTIES OF MULTIVARIATE TIME SERIES
229 7.3. ESTIMATION OF THE MEAN AND COVARIANCE FUNCTION 234 7.3.1.
ESTIMATION OF FJ, 234 7.3.2. ESTIMATION OF F(H) 235 7.3.3. TESTING FOR
INDEPENDENCE OFTWO STATIONARY TIME SERIES . 237 7.3.4. BARTLETT'S
FORMULA 238 7.4. MULTIVARIATE ARMA PROCESSES 241 7.4.1. THE COVARIANCE
MATRIX FUNCTION OF A CAUSAL ARMA PROCESS 244 7.5. BEST LINEAR PREDICTORS
OF SECOND-ORDER RANDOM VECTORS 244 7.6. MODELING AND FORECASTING WITH
MULTIVARIATE AR PROCESSES 246 7.6.1. ESTIMATION FOR AUTOREGRESSIVE
PROCESSES USING WHITTLE'S ALGORITHM 247 7.6.2. FORECASTING MULTIVARIATE
AUTOREGRESSIVE PROCESSES 250 7.7. COINTEGRATION 254 PROBLEMS 256 8.
STATE-SPACE MODELS 259 8.1. STATE-SPACE REPRESENTATIONS 260 8.2. THE
BASIC STRUCTURAL MODEL 263 8.3. STATE-SPACE REPRESENTATION OF ARIMA
MODELS 267 8.4. THE KAIMAN RECURSIONS 271 8.5. ESTIMATION FOR
STATE-SPACE MODELS 277 8.6. STATE-SPACE MODELS WITH MISSING OBSERVATIONS
283 8.7. THE EM ALGORITHM 289 8.8. GENERALIZED STATE-SPACE MODELS 292
8.8.1. PARAMETER-DRIVEN MODELS 292 XII CONTENTS 8.8.2.
OBSERVATION-DRIVEN MODELS 299 PROBLEMS 311 9. FORECASTING TECHNIQUES 317
9.1. THE ARAR ALGORITHM 318 9.1.1. MEMORY SHORTENING 318 9.1.2. FITTING
A SUBSET AUTOREGRESSION 319 9.1.3. FORECASTING 320 9.1.4. APPLICATION OF
THE ARAR ALGORITHM 321 9.2. THE HOLT-WINTERS ALGORITHM 322 9.2.1. THE
ALGORITHM 322 9.2.2. HOLT-WINTERS AND ARIMA FORECASTING 324 9.3. THE
HOLT-WINTERS SEASONAL ALGORITHM 326 9.3.1. THE ALGORITHM 326 9.3.2.
HOLT-WINTERS SEASONAL AND ARIMA FORECASTING 328 9.4. CHOOSING A
FORECASTING ALGORITHM 328 PROBLEMS 330 10. FURTHER TOPICS 331 10.1.
TRANSFER FUNCTION MODELS 331 10.1.1. PREDICTION BASED ON A TRANSFER
FUNCTION MODEL 337 10.2. INTERVENTION ANALYSIS 340 10.3. NONLINEAR
MODELS 343 10.3.1. DEVIATIONS FROM LINEARITY 344 10.3.2. CHAOTIC
DETERMINISTIC SEQUENCES 345 10.3.3. DISTINGUISHING BETWEEN WHITE NOISE
AND IID SEQUENCES 347 10.3.4. THREE USEFUL CLASSES OF NONLINEAR MODELS
348 10.3.5. MODELING VOLATILITY 349 10A. CONTINUOUS-TIME MODELS 357
10.5. LONG-MEMORY MODELS 361 PROBLEMS 365 A. RANDOM VARIABLES AND
PROBABILITY DISTRIBUTIONS 369 A.L. DISTRIBUTION FUNCTIONS AND
EXPECTATION 369 A.2. RANDOM VECTORS 374 A.3. THE MULTIVARIATE NORMAL
DISTRIBUTION 377 PROBLEMS 381 CONTENTS XIII B. STATISTICAL COMPLEMENTS
383 B.L. LEAST SQUARES ESTIMATION 383 B. 1.1. THE GAUSS-MARKOV THEOREM
385 B.L.2. GENERALIZED LEAST SQUARES 386 B.2. MAXIMUM LIKELIHOOD
ESTIMATION 386 B.2.1. PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS 387
B.3. CONFIDENCE INTERVALS 388 B.3.1. LARGE-SAMPLE CONFIDENCE REGIONS 388
B.4. HYPOTHESIS TESTING 389 B .4.1. ERROR PROBABILITIES 390 B.4.2.
LARGE-SAMPLE TESTS BASED ON CONFIDENCE REGIONS 390 C. MEAN SQUARE
CONVERGENCE 393 C.L. THE CAUCHY CRITERION 393 D. AN ITSM TUTORIAL 395
D.I. GETTING STARTED 396 D.L.L.RUNNINGLTSM 396 D.2. PREPARING YOUR DATA
FOR MODELING 396 D.2.1. ENTERING DATA 397 D.2.2. INFORMATION 397 D.2.3.
FILING DATA 397 D.2.4. PLOTTING DATA 398 D.2.5. TRANSFORMING DATA 398
D.3. FINDING A MODEL FOR YOUR DATA 403 D.3.1. AUTOFIT 403 D.3.2. THE
SAMPLE ACF AND PACF 403 D.3.3. ENTERING A MODEL 404 D.3.4. PRELIMINARY
ESTIMATION 406 D.3.5. THE AICC STATISTIC 408 D.3.6. CHANGING YOUR MODEL
408 D.3.7. MAXIMUM LIKELIHOOD ESTIMATION 409 D.3.8. OPTIMIZATION RESULTS
410 D.4. TESTING YOUR MODEL 411 D.4.1. PLOTTING THE RESIDUAIS 412 D.4.2.
ACF/PACF OF THE RESIDUAIS 412 D.4.3. TESTING FOR RANDOMNESS OF THE
RESIDUAIS 414 D.5. PREDICTION 415 D.5.1. FORECAST CRITERIA 415 D.5.2.
FORECAST RESULTS 415 XIV CONTENTS D.6. MODEL PROPERTIES 416 D.6.1. ARMA
MODELS 417 D.6.2. MODEL ACF, PACF 418 D.6.3. MODEL REPRESENTATIONS 419
D.6.4. GENERATING REALIZATIONS OF A RANDOM SERIES 420 D.6.5. SPECTRAL
PROPERTIES 421 D.7. MULTIVARIATE TIME SERIES 421 REFERENCES 423 INDEX
429 |
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| author | Brockwell, Peter J. 1937-2023 Davis, Richard A. 1952- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Brockwell, Peter J. 1937-2023 Verfasser (DE-588)171133188 aut Introduction to time series and forecasting [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis 2. ed. New York, NY [u.a.] Springer 2002 XIV, 434 S. graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Systemvoraussetzungen der CD-ROM-Beil.: IBM PC or equivalent; 5 MB of hard disk space;. - Windows 95, NT 4.0 or later versions Zeitreihenanalyse - Lehrbuch Prognose (DE-588)4047390-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Prognose (DE-588)4047390-9 s Zeitreihenanalyse (DE-588)4067486-1 s 1\p DE-604 Davis, Richard A. 1952- Verfasser (DE-588)173920608 aut HEBIS Datenaustausch Mainz application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009831956&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brockwell, Peter J. 1937-2023 Davis, Richard A. 1952- Introduction to time series and forecasting [includes ITSM 2000] Zeitreihenanalyse - Lehrbuch Prognose (DE-588)4047390-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4047390-9 (DE-588)4067486-1 (DE-588)4123623-3 |
| title | Introduction to time series and forecasting [includes ITSM 2000] |
| title_auth | Introduction to time series and forecasting [includes ITSM 2000] |
| title_exact_search | Introduction to time series and forecasting [includes ITSM 2000] |
| title_full | Introduction to time series and forecasting [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis |
| title_fullStr | Introduction to time series and forecasting [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis |
| title_full_unstemmed | Introduction to time series and forecasting [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis |
| title_short | Introduction to time series and forecasting |
| title_sort | introduction to time series and forecasting includes itsm 2000 |
| title_sub | [includes ITSM 2000] |
| topic | Zeitreihenanalyse - Lehrbuch Prognose (DE-588)4047390-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Zeitreihenanalyse - Lehrbuch Prognose Zeitreihenanalyse Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009831956&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brockwellpeterj introductiontotimeseriesandforecastingincludesitsm2000 AT davisricharda introductiontotimeseriesandforecastingincludesitsm2000 |