Time series: theory and methods
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1996
|
| Edition: | 2. ed., 5., corr. print. |
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 577 S. graph. Darst. |
| ISBN: | 3540974296 0387974296 |
Staff View
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| 100 | 1 | |a Brockwell, Peter J. |d 1937-2023 |e Verfasser |0 (DE-588)171133188 |4 aut | |
| 245 | 1 | 0 | |a Time series |b theory and methods |c Peter J. Brockwell ; Richard A. Davis |
| 250 | |a 2. ed., 5., corr. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XVI, 577 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1806866207803965440 |
|---|---|
| adam_text |
PETER J. BROCKWELL
RICHARD A. DAVIS
TIME SERIES:
THEOR
Y AN
D METHOD
S
SECOND EDITION
WITH 124 ILLUSTRATIONS
SPRINGE
R
CONTENT
S
PREFACE TO THE SECOND EDITION
PREFACE TO THE FIRST EDITION
VN
IX
CHAPTER 1
STATIONAR
Y TIM
E SERIES 1
§1.1 EXAMPLES OF TIME SERIES 1
§1.2 STOCHASTIC PROCESSES 8
§1.3 STATIONARITY AND STRICT STATIONARITY 11
§1.4 THE ESTIMATION AND ELIMINATION OF TREND AND SEASONAL COMPONENTS 14
§1.5 THE AUTOCOVARIANCE FUNCTION OF A STATIONARY PROCESS 25
§1.6 THE MULTIVARIATE NORMAL DISTRIBUTION 32
§1.7* APPLICATIONS OF KOLMOGOROV'S THEOREM 37
PROBLEMS 39
CHAPTER 2
HUBER
T SPACES 42
§2.1 INNER-PRODUCT SPACES AND THEIR PROPERTIES 42
§2.2 HUBERT SPACES 46
§2.3 THE PROJECTION THEOREM 48
§2.4 ORTHONORMAL SETS 54
§2.5 PROJECTION IN W 58
§2.6 LINEAR REGRESSION AND THE GENERAL LINEAR MODEL 60
§2.7 MEAN SQUARE CONVERGENCE, CONDITIONAL EXPECTATION AND BEST
LINEAR PREDICTION IN L
2
(Q, &, P) 62
§2.8 FOURIER SERIES 65
§2.9 HUBERT SPACE ISOMORPHISMS 67
§2.10* THECOMPLETENESSOFL
2
(Q,,^",P) 68
§2.11* COMPLEMENTARY RESULTS FOR FOURIER SERIES 69
PROBLEMS 73
XIV
CONTENTS
CHAPTER 3
STATIONAR
Y ARMA PROCESSES 77
§3.1 CAUSAL AND INVERTIBLE ARMA PROCESSES 77
§3.2 MOVING AVERAGE PROCESSES OF INFINITE ORDER 89
§3.3 COMPUTING THE AUTOCOVARIANCE FUNCTION OF AN ARMA(P, Q) PROCESS 91
§3.4 THE PARTIAL AUTOCORRELATION FUNCTION 98
§3.5 THE AUTOCOVARIANCE GENERATING FUNCTION 103
§3.6* HOMOGENEOUS LINEAR DIFFERENCE EQUATIONS WITH
CONSTANT COEFFICIENTS 105
PROBLEMS 110
CHAPTER 4
TH
E SPECTRAL REPRESENTATIO
N OF A STATIONAR
Y PROCESS 114
§4.1 COMPLEX-VALUED STATIONARY TIME SERIES 114
§4.2 THE SPECTRAL DISTRIBUTION OF A LINEAR COMBINATION OF SINUSOIDS 116
§4.3 HERGLOTZ'S THEOREM 117
§4.4 SPECTRAL DENSITIES AND ARMA PROCESSES 122
§4.5* CIRCULANTS AND THEIR EIGENVALUES 133
§4.6* ORTHOGONAL INCREMENT PROCESSES ON [ - N, 7T] 138
§4.7* INTEGRATION WITH RESPECT TO AN ORTHOGONAL INCREMENT PROCESS 140
§4.8* THE SPECTRAL REPRESENTATION 143
§4.9* INVERSION FORMULAE 150
§4.10* TIME-INVARIANT LINEAR FILTERS 152
§4.11 * PROPERTIES OF THE FOURIER APPROXIMATION HYY TO 7
(V| W]
157
PROBLEMS 159
CHAPTER 5
PREDICTIO
N OF STATIONAR
Y PROCESSES 166
§5.1 THE PREDICTION EQUATIONS IN THE TIME DOMAIN 166
§5.2 RECURSIVE METHODS FOR COMPUTING BEST LINEAR PREDICTORS 169
§5.3 RECURSIVE PREDICTION OF AN ARMA(P, Q) PROCESS 175
§5.4 PREDICTION OF A STATIONARY GAUSSIAN PROCESS; PREDICTION BOUNDS 182
§5.5 PREDICTION OF A CAUSAL INVERTIBLE ARMA PROCESS IN
TERMS OF X
P
- OO J N 182
§5.6* PREDICTION IN THE FREQUENCY DOMAIN 185
§5.7* THE WOLD DECOMPOSITION 187
§5.8* KOLMOGOROV'S FORMULA 191
PROBLEMS 192
CHAPTER 6*
ASYMPTOTIC THEOR
Y 198
§6.1 CONVERGENCE IN PROBABILITY 198
§6.2 CONVERGENCE IN R
LH
MEAN, R 0 202
§6.3 CONVERGENCE IN DISTRIBUTION 204
§6.4 CENTRAL LIMIT THEOREMS AND RELATED RESULTS 209
PROBLEMS 215
CONTENT
S
XV
CHAPTER 7
ESTIMATIO
N OF TH
E MEA
N AN
D TH
E AUTOCOVARIANC
E FUNCTIO
N 218
§7.1 ESTIMATIO
N OF N 218
§7.2 ESTIMATIO
N OF Y ( YY) AN
D P
( YY) 220
§7.3* DERIVATIO
N OF TH
E ASYMPTOTIC DISTRIBUTION
S 225
PROBLEM
S 236
CHAPTER 8
ESTIMATIO
N FO
R ARM
A MODEL
S 238
§8.1 TH
E YULE-WALKE
R EQUATION
S AN
D PARAMETE
R ESTIMATIO
N FOR
AUTOREGRESSIVE PROCESSES 239
§8.2 PRELIMINAR
Y ESTIMATIO
N FOR AUTOREGRESSIVE PROCESSES USIN
G TH
E
DURBIN-LEVINSO
N ALGORITHM 241
§8.3 PRELIMINAR
Y ESTIMATIO
N FOR MOVIN
G AVERAGE PROCESSES USIN
G TH
E
INNOVATION
S ALGORITHM 245
§8.4 PRELIMINAR
Y ESTIMATIO
N FOR ARMA(P
, Q) PROCESSES 250
§8.5 REMARK
S O
N ASYMPTOTI
C EFFICIENCY 253
§8.6 RECURSIVE CALCULATIO
N OF TH
E LIKELIHOO
D OF A
N ARBITRAR
Y
ZERO-MEA
N GAUSSIA
N PROCESS 254
§8.7 MAXIMU
M LIKELIHOOD AN
D LEAST SQUARE
S ESTIMATIO
N FOR
ARM
A PROCESSES 256
§8.8 ASYMPTOTIC PROPERTIE
S OF TH
E MAXIMU
M LIKELIHOOD ESTIMATOR
S 258
§8.9 CONFIDENCE INTERVAL
S FOR TH
E PARAMETER
S OF A CAUSA
L INVERTIBL
E
ARM
A PROCES
S 260
§8.10* ASYMPTOTI
C BEHAVIOR OF TH
E YULE-WALKE
R ESTIMATE
S 262
§8.11* ASYMPTOTIC NORMALIT
Y OF PARAMETE
R ESTIMATOR
S 265
PROBLEM
S 269
CHAPTER 9
MODE
L BUILDIN
G AN
D FORECASTIN
G WIT
H ARIM
A PROCESSE
S 273
§9.1 ARIM
A MODEL
S FOR NON-STATIONAR
Y TIM
E SERIES 274
§9.2 IDENTIFICATION TECHNIQUE
S 284
§9.3 ORDE
R SELECTION 301
§9.4 DIAGNOSTI
C CHECKING 306
§9.5 FORECASTIN
G ARIM
A MODEL
S 314
§9.6 SEASONAL ARIM
A MODEL
S 320
PROBLEM
S 326
CHAPTER 10
INFERENC
E FO
R TH
E SPECTRU
M OF A STATTONAR
Y PROCES
S 330
§10.1 TH
E PERIODOGRA
M 331
§10.2 TESTINGFORTHEPRESENCEOFHIDDE
N PERIODICITIES 334
§10.3 ASYMPTOTI
C PROPERTIE
S OF TH
E PERIODOGRA
M 342
§10.4 SMOOTHIN
G TH
E PERIODOGRA
M 350
§10.5 CONFIDENCE INTERVAL
S FOR TH
E SPECTRUM 362
§10.6 AUTOREGRESSIVE, MAXIMU
M ENTROPY
, MOVIN
G AVERAGE AN
D
MAXIMU
M LIKELIHOOD ARM
A SPECTRAL ESTIMATOR
S 365
§10.7 TH
E FAS
T FOURIE
R TRANSFORM (FFT
) ALGORITHM 373
XVI
CONTENTS
§10.8* DERIVATION OF THE ASYMPTOTIC BEHAVIOR OF THE MAXIMUM
LIKELIHOOD AND LEAST SQUARES ESTIMATORS OF THE COEFFICIENTS OF
AN ARMA PROCESS 375
PROBLEMS 396
CHAPTER 11
MULTIVARIATE TIM
E SERIES 401
§11.1 SECOND ORDER PROPERTIES OF MULTIVARIATE TIME SERIES 402
§11.2 ESTIMATION OF THE MEAN AND COVARIANCE FUNCTION 405
§11.3 MULTIVARIATE ARMA PROCESSES 417
§11.4 BEST LINEAR PREDICTORS OF SECOND ORDER RANDOM VECTORS 421
§11.5 ESTIMATION FOR MULTIVARIATE ARMA PROCESSES 430
§11.6 THE CROSS SPECTRUM 434
§11.7 ESTIMATING THE CROSS SPECTRUM 443
§11.8* THE SPECTRAL REPRESENTATION OF A MULTIVARIATE STATIONARY
TIME SERIES 454
PROBLEMS 459
CHAPTER 12
STATE-SPACE MODELS AND THE KAIMAN RECURSIONS 463
§12.1 STATE-SPACE MODELS 463
§12.2 THE KAIMAN RECURSIONS 474
§12.3 STATE-SPACE MODELS WITH MISSING OBSERVATIONS 482
§12.4 CONTROLLABILITY AND OBSERVABILITY 489
§12.5 RECURSIVE BAYESIAN STATE ESTIMATION 498
PROBLEMS 501
CHAPTER 13
FURTHE
R TOPIC
S 506
§13.1 TRANSFER FUNCTION MODELLING 506
§13.2 LONG MEMORY PROCESSES 520
§13.3 LINEAR PROCESSES WITH INFINITE VARIANCE 535
§13.4 THRESHOLD MODELS 545
PROBLEMS 552
APPENDIX: DAT
A SETS 555
BIBLIOGRAPHY 561
INDEX 567 |
| any_adam_object | 1 |
| author | Brockwell, Peter J. 1937-2023 Davis, Richard A. |
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| dewey-full | 519.5/5 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| spelling | Brockwell, Peter J. 1937-2023 Verfasser (DE-588)171133188 aut Time series theory and methods Peter J. Brockwell ; Richard A. Davis 2. ed., 5., corr. print. New York [u.a.] Springer 1996 XVI, 577 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Análisis de series de tiempo Models, Theoretical Research methods Statistics as Topic methods Stochastic Processes Time Factors Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Davis, Richard A. Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007471628&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brockwell, Peter J. 1937-2023 Davis, Richard A. Time series theory and methods Análisis de series de tiempo Models, Theoretical Research methods Statistics as Topic methods Stochastic Processes Time Factors Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4123623-3 |
| title | Time series theory and methods |
| title_auth | Time series theory and methods |
| title_exact_search | Time series theory and methods |
| title_full | Time series theory and methods Peter J. Brockwell ; Richard A. Davis |
| title_fullStr | Time series theory and methods Peter J. Brockwell ; Richard A. Davis |
| title_full_unstemmed | Time series theory and methods Peter J. Brockwell ; Richard A. Davis |
| title_short | Time series |
| title_sort | time series theory and methods |
| title_sub | theory and methods |
| topic | Análisis de series de tiempo Models, Theoretical Research methods Statistics as Topic methods Stochastic Processes Time Factors Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Análisis de series de tiempo Models, Theoretical Research methods Statistics as Topic methods Stochastic Processes Time Factors Time-series analysis Zeitreihenanalyse Lehrbuch |
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