Time series: theory and methods
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2006
|
| Edition: | 2. ed., [Nachdr.] |
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVI, 577 S. graph. Darst. |
| ISBN: | 9781441904003 3540974296 0387974296 9780387974293 9781441903198 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV021999550 | ||
| 003 | DE-604 | ||
| 005 | 20250527 | ||
| 007 | t| | ||
| 008 | 061208s2006 gw d||| |||| 00||| eng d | ||
| 020 | |a 9781441904003 |c Paperback |9 978-1-4419-0400-3 | ||
| 020 | |a 3540974296 |9 3-540-97429-6 | ||
| 020 | |a 0387974296 |9 0-387-97429-6 | ||
| 020 | |a 9780387974293 |9 978-0-387-97429-3 | ||
| 020 | |a 9781441903198 |9 978-1-4419-0319-8 | ||
| 035 | |a (OCoLC)320199688 | ||
| 035 | |a (DE-599)BVBBV021999550 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-19 |a DE-29T |a DE-355 |a DE-824 |a DE-91G |a DE-N2 |a DE-83 |a DE-11 |a DE-473 |a DE-20 | ||
| 050 | 0 | |a QA280 | |
| 082 | 0 | |a 519.5/5 |2 20 | |
| 084 | |a QH 237 |0 (DE-625)141552: |2 rvk | ||
| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 084 | |a SK 845 |0 (DE-625)143262: |2 rvk | ||
| 084 | |a MAT 634f |2 stub | ||
| 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., [Nachdr.] | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2006 | |
| 300 | |a XVI, 577 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Time-series analysis | |
| 650 | 0 | 7 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Davis, Richard A. |d 1952- |e Verfasser |0 (DE-588)173920608 |4 aut | |
| 856 | 4 | |m Digitalisierung UB Regensburg |u https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |z Inhaltsverzeichnis | |
| 856 | 4 | |m Digitalisierung UB Regensburg |u https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |z Klappentext | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-015057838 | |
Record in the Search Index
| _version_ | 1833297577640984576 |
|---|---|
| adam_text | |
| adam_txt |
Contents
Prefece
to the Second Edition
vìi
Prefece
to the First Edition
ix
CHAPTER
1
Stationary Time 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
Hubert 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 R"
58
§2.6
Linear Regression and the General Linear Model
60
§2.7
Mean Square Convergence, Conditional Expectation and Best
Linear Prediction in LZ(Q, J% P)
62
§2.8
Fourier Series
65
§2.9
Hubert Space Isomorphisms
67
§2.10*
The Completeness of L2{O,
&,
P)
68
§2.11*
Complementary Results for Fourier Series
69
Problems
73
xiv
Contents
CHAPTER
3
Stationary
ARMA
Processes
77
§3.1
Causal and
Invertitile 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
The Spectral Representation of a Stationary 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
[—π, π]
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
й„
to
ƒ(„„,] 157
Problems
159
CHAPTER
5
Prediction of Stationary 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 ARM A(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 Xj,
-
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 Theory
198
§6.1
Convergence in Probability
198
§6.2
Convergence in rth Mean,
r
> 0 202
§6.3
Convergence in Distribution
204
§6.4
Central Limit Theorems and Related Results
209
Problems
215
Contents
CHAPTER
7
Estimation of the Mean and the Autocovariance Function
218
§7.1
Estimation of
μ
218
§7.2
Estimation of y(
- )
and p(
■ ) 220
§7.3*
Derivation of the Asymptotic Distributions
225
Problems
236
CHAPTER
8
Estimation for
ARMA
Models
238
§8.1
The Yule-Walker Equations and Parameter Estimation for
Autoregressive
Processes
239
§8.2
Preliminary Estimation for
Autoregressive
Processes Using the
Durbin-Levinson Algorithm
241
§8.3
Preliminary Estimation for Moving Average Processes Using the
Innovations Algorithm
245
§8.4
Preliminary Estimation for ARMA(p, q) Processes
250
§8.5
Remarks on Asymptotic Efficiency
253
§8.6
Recursive Calculation of the Likelihood of an Arbitrary
Zero-Mean Gaussian Process
254
§8.7
Maximum Likelihood and Least Squares Estimation for
ARMA
Processes
256
§8.8
Asymptotic Properties of the Maximum Likelihood Estimators
258
§8.9
Confidence Intervals for the Parameters of a Causal In
vertible
ARMA
Process
260
§8.10*
Asymptotic Behavior of the Yule-Walker Estimates
262
§8.11*
Asymptotic Normality of Parameter Estimators
265
Problems
269
CHAPTER
9
Model Building and Forecasting with ARIMA Processes
273
§9.1
ARIMA Models for Non-Stationary Time Series
274
§9.2
Identification Techniques
284
§9.3
Order Selection
301
§9.4
Diagnostic Checking
306
§9.5
Forecasting ARIMA Models
314
§9.6
Seasonal ARIMA Models
320
Problems
326
CHAPTER
10
Inference for the Spectrum of a Stationary Process
330
§10.1
The
Periodogram
331
§10.2
Testing for the Presence of Hidden Periodicities
334
§10.3
Asymptotic Properties of the
Periodogram
342
§10.4
Smoothing the
Periodogram
350
§10.5
Confidence Intervals for the Spectrum
362
§10.6
Autoregressive,
Maximum Entropy, Moving Average and
Maximum Likelihood
ARMA
Spectral Estimators
365
§10.7
The Fast Fourier 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 Time 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
Kalman
Recursions
463
§12.1
State-Space Models
463
§12.2
The
Kalman
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
Further Topics
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: Data Sets
555
Bibliography
561
Index
567
Time Series: Theory and Methods is a systematic account of linear time
series models and their application to the modeling and prediction of data
collected sequentially in time. The aim is to provide specific techniques
for handling data and at the same time to provide a thorough understanding
of the mathematical basis for the technique«. Both time and frequency
domain methods are discussed, but the book is written in such a way that
either approach could be emphasized. The book is intended to be a text for
graduate students in statistics, mathematics, engineering, and the natural
or social sciences. It contains substantial chapters on multivariate series
and state-space models (Including appiicatione of the
Kalman
recursions to
missing-value problems) and shorter accounts of special topics including
long-range dependence,
infinite
variance proceeees, and non-linear models.
Most of the programs used in the book are contained in the software pack¬
age ITSM2000, the student version of which Accompanies the authors'
introductory book, Introduction to Time Series and Forecasting, also
published by
Springer-verlag. |
| any_adam_object | |
| any_adam_object_boolean | 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- |
| author_role | aut aut |
| author_sort | Brockwell, Peter J. 1937-2023 |
| author_variant | p j b pj pjb r a d ra rad |
| building | Verbundindex |
| bvnumber | BV021999550 |
| callnumber-first | Q - Science |
| callnumber-label | QA280 |
| callnumber-raw | QA280 |
| callnumber-search | QA280 |
| callnumber-sort | QA 3280 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 830 SK 845 |
| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)320199688 (DE-599)BVBBV021999550 |
| 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 Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., [Nachdr.] |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV021999550</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20250527</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">061208s2006 gw d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441904003</subfield><subfield code="c">Paperback</subfield><subfield code="9">978-1-4419-0400-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540974296</subfield><subfield code="9">3-540-97429-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387974296</subfield><subfield code="9">0-387-97429-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387974293</subfield><subfield code="9">978-0-387-97429-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441903198</subfield><subfield code="9">978-1-4419-0319-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)320199688</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021999550</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-N2</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA280</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5/5</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 237</subfield><subfield code="0">(DE-625)141552:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 830</subfield><subfield code="0">(DE-625)143259:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 845</subfield><subfield code="0">(DE-625)143262:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 634f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brockwell, Peter J.</subfield><subfield code="d">1937-2023</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)171133188</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Time series</subfield><subfield code="b">theory and methods</subfield><subfield code="c">Peter J. Brockwell ; Richard A. Davis</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed., [Nachdr.]</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 577 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer series in statistics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Time-series analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zeitreihenanalyse</subfield><subfield code="0">(DE-588)4067486-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zeitreihenanalyse</subfield><subfield code="0">(DE-588)4067486-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Davis, Richard A.</subfield><subfield code="d">1952-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)173920608</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="u">https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="z">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="u">https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="z">Klappentext</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015057838</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV021999550 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:02:05Z |
| indexdate | 2025-05-27T18:00:13Z |
| institution | BVB |
| isbn | 9781441904003 3540974296 0387974296 9780387974293 9781441903198 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015057838 |
| oclc_num | 320199688 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-29T DE-355 DE-BY-UBR DE-824 DE-91G DE-BY-TUM DE-N2 DE-83 DE-11 DE-473 DE-BY-UBG DE-20 |
| owner_facet | DE-19 DE-BY-UBM DE-29T DE-355 DE-BY-UBR DE-824 DE-91G DE-BY-TUM DE-N2 DE-83 DE-11 DE-473 DE-BY-UBG DE-20 |
| physical | XVI, 577 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Brockwell, Peter J. 1937-2023 Verfasser (DE-588)171133188 aut Time series theory and methods Peter J. Brockwell ; Richard A. Davis 2. ed., [Nachdr.] New York [u.a.] Springer 2006 XVI, 577 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Hier auch später erschienene, unveränderte Nachdrucke 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. 1952- Verfasser (DE-588)173920608 aut Digitalisierung UB Regensburg https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Brockwell, Peter J. 1937-2023 Davis, Richard A. 1952- Time series theory and methods 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_exact_search_txtP | 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 | Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Time-series analysis Zeitreihenanalyse Lehrbuch |
| url | https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015057838&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brockwellpeterj timeseriestheoryandmethods AT davisricharda timeseriestheoryandmethods |