Introduction to time series modeling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2010
|
| Schriftenreihe: | Monographs on statistics and applied probability
114 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIII, 289 S. graph. Darst. |
| ISBN: | 9781584889212 |
Internformat
MARC
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| 100 | 1 | |a Kitagawa, Genshiro |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to time series modeling |c Genshiro Kitagawa |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2010 | |
| 300 | |a XXIII, 289 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs on statistics and applied probability |v 114 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a State-space methods | |
| 650 | 4 | |a Time-series analysis | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020423620 | ||
Datensatz im Suchindex
| _version_ | 1804143065639682048 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION AND PREPARATORY ANALYSIS 1
1 . 1 TIME SERIES DATA 1
1.2 CLASSIFICATION OF TIME SERIES 6
1.3 OBJECTIVES OF TIME SERIES ANALYSIS 8
1.4 PRE-PROCESSING OF TIME SERIES 8
1.4.1 TRANSFORMATION OF VARIABLES 9
1.4.2 DIFFERENCING 9
1.4.3 CHANGE FROM THE PREVIOUS MONTH (QUARTER) AND ANNUAL CHANGE 10
1.4.4 MOVING AVERAGE 11
1.5 ORGANIZATION OF THIS BOOK 1 3
2 THE COVARIANCE FUNCTION 17
2.1 THE DISTRIBUTION OF TIME SERIES AND STATIONARITY 17 2.2 THE
AUTOCOVARIANCE FUNCTION OF STATIONARY TIME SERIES 20 2.3 ESTIMATION OF
THE AUTOCOVARIANCE FUNCTION 21
2.4 MULTIVARIATE TIME SERIES AND SCATTERPLOTS 24
2.5 CROSS-COVARIANCE FUNCTION AND CROSS-CORRELATION FUNCTION 26
3 THE POWER SPECTRUM AND THE PERIODOGRAM 31
3.1 THE POWER SPECTRUM 31
3.2 THE PERIODOGRAM 36
3.3 AVERAGING AND SMOOTHING OF THE PERIODOGRAM 40 3.4 COMPUTATIONAL
METHOD OF PERIODOGRAM 44
3.5 COMPUTATION OF THE PERIODOGRAM BY FAST FOURIER TRANS- FORM 44
4 STATISTICAL MODELING 49
4.1 PROBABILITY DISTRIBUTIONS AND STATISTICAL MODELS 49
IMAGE 2
XX CONTENTS
4.2 K-L INFORMATION AND THE ENTROPY MAXIMIZATION PRINCI- PLE 54
4.3 ESTIMATION OF THE K-L INFORMATION AND LOG-LIKELIHOOD 56 4.4
ESTIMATION OF PARAMETERS BY THE MAXIMUM LIKELIHOOD METHOD 58
4.5 AIC (AKAIKE INFORMATION CRITERION) 62
4.5.1 EVALUATION OF C 64
4.5.2 EVALUATION OF C 3 65
4.5.3 EVALUATION OF C 2 66
4.5.4 EVALUATION OF C AND AIC 66
4.6 TRANSFORMATION OF DATA 66
5 THE LEAST SQUARES METHOD 71
5.1 REGRESSION MODELS AND THE LEAST SQUARES METHOD 71 5.2 HOUSEHOLDER
TRANSFORMATION 73
5.3 SELECTION OF ORDER BY AIC 75
5.4 ADDITION OF DATA AND SUCCESSIVE HOUSEHOLDER REDUCTION 78 5.5
VARIABLE SELECTION BY AIC 79
6 ANALYSIS OF TIME SERIES USING ARMA MODELS 83
6.1 ARMA MODEL 83
6.2 THE IMPULSE RESPONSE FUNCTION 84
6.3 THE AUTOCOVARIANCE FUNCTION 85
6.4 THE RELATION BETWEEN AR COEFFICIENTS AND THE PAR- COR 88
6.5 THE POWER SPECTRUM OF THE ARMA PROCESS 88
6.6 THE CHARACTERISTIC EQUATION 92
6.7 THE MULTIVARIATE AR MODEL 93
7 ESTIMATION OF AN AR MODEL 103
7.1 FITTING AN AR MODEL 103
7.2 YULE-WALKER METHOD AND LEVINSON S ALGORITHM 105 7.3 ESTIMATION OF AN
AR MODEL BY THE LEAST SQUARES METHOD 106
7.4 ESTIMATION OF AN AR MODEL BY THE PARCOR METHOD 108 7.5 LARGE SAMPLE
DISTRIBUTION OF THE ESTIMATES 111
7.6 ESTIMATION OF A MULTIVARIATE AR MODEL BY THE YULE- WALKER METHOD 113
7.7 ESTIMATION OF A MULTIVARIATE AR MODEL BY THE LEAST SQUARES METHOD
117
IMAGE 3
CONTENTS XXI
8 THE LOCALLY STATIONARY AR MODEL 123
8.1 LOCALLY STATIONARY AR MODEL 123
8.2 AUTOMATIC PARTITIONING OF THE TIME INTERVAL INTO AN ARBITRARY NUMBER
OF SUBINTERVALS 125
8.3 PRECISE ESTIMATION OF A CHANGE POINT 1 30
9 ANALYSIS OF TIME SERIES WITH A STATE-SPACE MODEL 135 9.1 THE
STATE-SPACE MODEL 135
9.2 STATE ESTIMATION VIA THE KALMAN FILTER 138
9.3 SMOOTHING ALGORITHMS 140
9.4 INCREASING HORIZON PREDICTION OF THE STATE 140
9.5 PREDICTION OF TIME SERIES 141
9.6 LIKELIHOOD COMPUTATION AND PARAMETER ESTIMATION FOR A TIME SERIES
MODEL 144
9.7 INTERPOLATION OF MISSING OBSERVATIONS 147
10 ESTIMATION OF THE ARMA MODEL 151
10.1 STATE-SPACE REPRESENTATION OF THE ARMA MODEL 151 10.2 INITIAL STATE
OF AN ARMA MODEL 152
10.3 MAXIMUM LIKELIHOOD ESTIMATE OF AN ARMA MODEL 153 10.4 INITIAL
ESTIMATES OF PARAMETERS 154
11 ESTIMATION OF TRENDS 159
11.1 THE POLYNOMIAL TREND MODEL 159
11.2 TREND COMPONENT MODEL-MODEL FOR PROBABILISTIC STRUCTURAL CHANGES
162
11.3 TREND MODEL 165
12 THE SEASONAL ADJUSTMENT MODEL 173
12.1 SEASONAL COMPONENT MODEL 173
12.2 STANDARD SEASONAL ADJUSTMENT MODEL 176
12.3 DECOMPOSITION INCLUDING AN AR COMPONENT 179 12.4 DECOMPOSITION
INCLUDING A TRADING-DAY EFFECT 1 84
13 TIME-VARYING COEFFICIENT AR MODEL 189
13.1 TIME-VARYING VARIANCE MODEL 189
13.2 TIME-VARYING COEFFICIENT AR MODEL 192
13.3 ESTIMATION OF THE TIME-VARY ING SPECTRUM 197
13.4 THE ASSUMPTION ON SYSTEM NOISE FOR THE TIME-VARYING COEFFICIENT AR
MODEL 198
13.5 ABRUPT CHANGES OF COEFFICIENTS 199
IMAGE 4
XXII CONTENTS
14 NON-GAUSSIAN STATE-SPACE MODEL 203
14.1 NECESSITY OF NON-GAUSSIAN MODELS 203
14.2 NON-GAUSSIAN STATE-SPACE MODELS AND STATE ESTIMATION 204 14.3
NUMERICAL COMPUTATION OF THE STATE ESTIMATION FORMULA 206 14.4
NON-GAUSSIAN TREND MODEL 209
14.5 A TIME-VARYING VARIANCE MODEL 213
14.6 APPLICATIONS OF NON-GAUSSIAN STATE-SPACE MODEL 217 14.6.1
PROCESSING OF THE OUTLIERS BY A MIXTURE OF GAUSSIAN DISTRIBUTIONS 217
14.6.2 A NONSTATIONARY DISCRETE PROCESS 218
14.6.3 A DIRECT METHOD OF ESTIMATING THE TIME-VARYING VARIANCE 219
15 THE SEQUENTIAL MONTE CARLO FILTER 221
15.1 THE NONLINEAR NON-GAUSSIAN STATE-SPACE MODEL AND APPROXIMATIONS OF
DISTRIBUTIONS 221
15.2 MONTE CARLO FILTER 225
15.2.1 ONE-STEP-AHEAD PREDICTION 225
15.2.2 FILTERING 225
15.2.3 ALGORITHM FOR THE MONTE CARLO FILTER 226
15.2.4 LIKELIHOOD OF A MODEL 226
15.2.5 RE-SAMPLING METHOD 227
15.2.6 NUMERICAL EXAMPLES 228
15.3 MONTE CARLO SMOOTHING METHOD 231
15.4 NONLINEAR SMOOTHING 233
16 SIMULATION 237
16.1 GENERATION OF UNIFORM RANDOM NUMBERS 237
16.2 GENERATION OF GAUSSIAN WHITE NOISE 239
16.3 SIMULATION USING A STATE-SPACE MODEL 241
16.4 SIMULATION WITH NON-GAUSSIAN MODEL 243
16.4.1 X 2 DISTRIBUTION 244
16.4.2 CAUCHY DISTRIBUTION 244
16.4.3 ARBITRARY DISTRIBUTION 244
A ALGORITHMS FOR NONLINEAR OPTIMIZATION 249
B DERIVATION OF LEVINSON S ALGORITHM 251
IMAGE 5
CONTENTS XXIII
C DERIVATION OF THE KALMAN FILTER
AND SMOOTHER ALGORITHMS 255
C.I KALMAN FILTER 255
C.2 SMOOTHING 256
D ALGORITHM FOR THE MONTE CARLO FILTER 259
D.I ONE-STEP-AHEAD PREDICTION 259
D.2 FILTER 260
D.3 SMOOTHING 261
ANSWERS TO THE PROBLEMS 263
BIBLIOGRAPHY 277
INDEX 285
|
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| id | DE-604.BV036501197 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:41:44Z |
| institution | BVB |
| isbn | 9781584889212 |
| language | English |
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| spelling | Kitagawa, Genshiro Verfasser aut Introduction to time series modeling Genshiro Kitagawa Boca Raton [u.a.] Chapman & Hall/CRC 2010 XXIII, 289 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 114 Includes bibliographical references and index State-space methods Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Monographs on statistics and applied probability 114 (DE-604)BV002494005 114 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020423620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kitagawa, Genshiro Introduction to time series modeling Monographs on statistics and applied probability State-space methods Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 |
| title | Introduction to time series modeling |
| title_auth | Introduction to time series modeling |
| title_exact_search | Introduction to time series modeling |
| title_full | Introduction to time series modeling Genshiro Kitagawa |
| title_fullStr | Introduction to time series modeling Genshiro Kitagawa |
| title_full_unstemmed | Introduction to time series modeling Genshiro Kitagawa |
| title_short | Introduction to time series modeling |
| title_sort | introduction to time series modeling |
| topic | State-space methods Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | State-space methods Time-series analysis Zeitreihenanalyse |
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