Introduction to time series and forecasting: includes CD-ROM ; [includes ITSM 2000]
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin [u.a.]
Springer
2003
|
| Ausgabe: | 2. ed., corr. print. |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 434 S. graph. Darst. 1 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: | 0387953515 |
Internformat
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| 245 | 1 | 0 | |a Introduction to time series and forecasting |b includes CD-ROM ; [includes ITSM 2000] |c Peter J. Brockwell ; Richard A. Davis |
| 250 | |a 2. ed., corr. print. | ||
| 264 | 1 | |a New York ; Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XIV, 434 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1806866207640387584 |
|---|---|
| adam_text |
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
μ
58
2.4.2.
Estimation of
γ
(·)
and
ρ
(·) 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.
The ACF and PACF of an ARMAC/j,^) 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
=
Ι,.,.,η}
165
5.3.2.
The Sample ACF of the Residuals
166
5.3.3.
Tests for Randomness of the Residuals
166
5.4.
Forecasting
167
5.5.
Order Selection
169
5.5.1.
The FPE Criterion
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
x¡
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
S
ARIMA 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
μ
234
7.3.2.
Estimation of
Γ
(A)
235
7.3.3.
Testing for Independence of Two 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
Kalman
Recursions
271
8.5.
Estimation For State-Space Models
277
8.6.
State-Space Models withJMissing 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
10.4.
Continuous-Time Models
357
10.5.
Long-Memory Models
361
Problems
365
A. Random Variables and Probability Distributions
369
A.
1.
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.I. Least Squares Estimation
383
B.I.I. The Gauss-Markov Theorem
385
B.
1.2.
Generalized Least Squares
386
B.2. Maximum Likelihood Estimation
386
B.2.
1.
Properties of Maximum Likelihood Estimators
387
B.3. Confidence Intervals
388
В
.3.1.
Large-Sample Confidence Regions
388
B.4. Hypothesis Testing
389
В
.4.1.
Error Probabilities
390
B.4.2. Large-Sample Tests Based on Confidence Regions
390
C. Mean Square Convergence
393
C.I. The Cauchy Criterion
393
D. An ITSM Tutorial
395
D.I.
Getting Started
396
D.I.I. Running ITSM
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 Residuals
412
D.4.2. ACF/PACF of the Residuals
412
D.4.3. Testing for Randomness of the Residuals
414
D.5. Prediction
415
D.5.1. Forecast Criteria
415
D.5.2. Forecast Results
415
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 |
| any_adam_object | 1 |
| author | Brockwell, Peter J. 1937-2023 Davis, Richard A. 1952- |
| author_GND | (DE-588)171133188 (DE-588)173920608 |
| author_facet | Brockwell, Peter J. 1937-2023 Davis, Richard A. 1952- |
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| callnumber-sort | QA 3280 B757 42002 |
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| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)66747532 (DE-599)BVBBV017093824 |
| dewey-full | 519.5/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 |
| dewey-search | 519.5/5 |
| dewey-sort | 3519.5 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., corr. print. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-09T00:04:55Z |
| institution | BVB |
| isbn | 0387953515 |
| language | German |
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| spelling | Brockwell, Peter J. 1937-2023 Verfasser (DE-588)171133188 aut Introduction to time series and forecasting includes CD-ROM ; [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis 2. ed., corr. print. New York ; Berlin [u.a.] Springer 2003 XIV, 434 S. graph. Darst. 1 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 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 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010309136&sequence=000002&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 CD-ROM ; [includes ITSM 2000] 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 CD-ROM ; [includes ITSM 2000] |
| title_auth | Introduction to time series and forecasting includes CD-ROM ; [includes ITSM 2000] |
| title_exact_search | Introduction to time series and forecasting includes CD-ROM ; [includes ITSM 2000] |
| title_full | Introduction to time series and forecasting includes CD-ROM ; [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis |
| title_fullStr | Introduction to time series and forecasting includes CD-ROM ; [includes ITSM 2000] Peter J. Brockwell ; Richard A. Davis |
| title_full_unstemmed | Introduction to time series and forecasting includes CD-ROM ; [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 cd rom includes itsm 2000 |
| title_sub | includes CD-ROM ; [includes ITSM 2000] |
| topic | Prognose (DE-588)4047390-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Prognose Zeitreihenanalyse Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010309136&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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