Mathematical foundations of time series analysis: a concise introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2017]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 307 Seiten Diagramme |
| ISBN: | 9783319743783 9783030089757 |
Staff View
MARC
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| 100 | 1 | |a Beran, Jan |d 1959- |0 (DE-588)141540060 |4 aut | |
| 245 | 1 | 0 | |a Mathematical foundations of time series analysis |b a concise introduction |c Jan Beran |
| 264 | 1 | |a Cham |b Springer |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a ix, 307 Seiten |b Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Statistics | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Statistics | |
| 650 | 4 | |a Statistical Theory and Methods | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction......................................................... 1
1.1 What Is a Time Series?............................................ 1
1.2 Time Series Versus iid Data....................................... 2
2 Typical Assumptions.................................................. 5
2.1 Fundamental Properties............................................ 5
2.1.1 Ergodic Property with a Constant Limit................. 5
2.1.2 Strict Stationarity ....................................... 7
2.1.3 Weak Stationarity.......................................... 8
2.1.4 Weak Stationarity and Hilbert Spaces................... 11
2.1.5 Ergodic Processes......................................... 32
2.1.6 Sufficient Conditions for the a.s. Ergodic Property
with a Constant Limit..................................... 34
2.1.7 Sufficient Conditions for the L2-Ergodic Property
with a Constant Limit..................................... 35
2.2 Specific Assumptions........................................... 39
2.2.1 Gaussian Processes ....................................... 39
2.2.2 Linear Processes in L2(£2)............................. 40
2.2.3 Linear Processes with E(Xf) = oo....................... 44
2.2.4 Multivariate Linear Processes............................. 48
2.2.5 Invertibility............................................. 49
2.2.6 Restrictions on the Dependence Structure.................. 63
3 Defining Probability Measures for Time Series........................ 69
3.1 Finite Dimensional Distributions................................. 69
3.2 Transformations and Equations.................................... 70
3.3 Conditions on the Expected Value ................................ 71
3.4 Conditions on the Autocovariance Function........................ 73
3.4.1 Positive Semidefinite Functions........................... 73
3.4.2 Spectral Distribution..................................... 77
3.4.3 Calculation and Properties of F and/.................... 86
vii
Contents
viii
4 Spectral Representation of Univariate Time Series.................... 101
4.1 Motivation.................................................... 101
4.2 Harmonic Processes............................................ 102
4.3 Extension to General Processes................................ 105
4.3.1 Stochastic Integrals with Respect toZ.................. 105
4.3.2 Existence and Definition of Z.......................... 112
4.3.3 Interpretation of the Spectral Representation.......... 122
4.4 Further Properties............................................ 122
4.4.1 Relationship Between Re Z and Im Z..................... 122
4.4.2 Frequency ............................................. 123
4.4.3 Overtones............................................... 124
4.4.4 Why Are Frequencies Restricted to the Range [—tt, 7r]?... 125
4.5 Linear Filters and the Spectral Representation................ 129
4.5.1 Effect on the Spectral Representation................... 129
4.5.2 Elimination of Frequency Bands.......................... 134
5 Spectral Representation of Real Valued Vector Time Series............ 137
5.1 Cross-Spectrum and Spectral Representation.................... 137
5.2 Coherence and Phase............................................ 146
6 Univariate ARM A Processes........................................... 161
6.1 Definition.................................................... 161
6.2 Stationary Solution........................................... 161
6.3 Causal Stationary Solution..................................... 166
6.4 Causal Invertible Stationary Solution ........................ 169
6.5 Aulocovariances of ARM A Processes ............................ 170
6.5.1 Calculation by Integration............................. 170
6.5.2 Calculation Using the Autocovariance Generating
Function................................................ 170
6.5.3 Calculation Using the Wold Representation............... 175
6.5.4 Recursive Calculation................................... 176
6.5.5 Asymptotic Decay ....................................... 177
6.6 Integrated, Seasonal and Fractional ARMA and ARIMA
Processes...................................................... 185
6.6.1 Integrated Processes.................................. 185
6.6.2 Seasonal ARMA Processes................................. 186
6.6.3 Fractional ARIMA Processes ............................. 187
6.7 Unit Roots, Spurious Correlation, Cointegration................ 200
7 Generalized Autoregressive Processes................................. 203
7.1 Definition of Generalized Autoregressive Processes............. 203
7.2 Stationary Solution of Generalized Autoregressive Equations... 204
7.3 Definition of VARMA Processes.................................. 209
7.4 Stationary Solution of VARMA Equations ........................ 211
7.5 Definition of GARCH Processes.................................. 213
7.6 Stationary Solution of GARCH Equations......................... 214
Contents
7.7 Definition of ARCHi ) Processes............................... 219
7.8 Stationary Solution of ARCHi ) liquations..................... 220
8 Prediction.......................................................... 223
8.1 Best Linear Prediction Gi en an Infinite Past................. 223
8.2 Predictability ............................................... 225
8.3 Construction of the Wold Decomposition f rom /................ 230
8.4 Best Linear Prediction Given a Pinite Past.................... 235
9 Inference for y and /* ......................................... 241
9.1 Location Lstimation......................................... 24 1
9.2 Linear Regression............................................. 244
9.3 Nonparametric Lstimation of y................................. 253
9.4 Nonparametric Lstimation of/.................................. 262
10 Parametric Lstimation............................................. 281
10.1 Gaussian and Quasi Maximum Likelihood Lstimation.............. 281
10.2 Whittle Approximation ........................................ 284
10.3 Autoregressive Approximation.................................. 287
10.4 Model Choice.................................................. 289
References............................................................... 293
Author Index............................................................. 299
Subject Index
303
|
| any_adam_object | 1 |
| author | Beran, Jan 1959- |
| author_GND | (DE-588)141540060 |
| author_facet | Beran, Jan 1959- |
| author_role | aut |
| author_sort | Beran, Jan 1959- |
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| bvnumber | BV044910783 |
| classification_rvk | SK 845 QH 237 |
| ctrlnum | (OCoLC)1032689721 (DE-599)BVBBV044910783 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV044910783 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:04:31Z |
| institution | BVB |
| isbn | 9783319743783 9783030089757 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030304326 |
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| owner_facet | DE-11 DE-355 DE-BY-UBR DE-521 DE-83 DE-573 |
| physical | ix, 307 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | Springer |
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| spelling | Beran, Jan 1959- (DE-588)141540060 aut Mathematical foundations of time series analysis a concise introduction Jan Beran Cham Springer [2017] © 2017 ix, 307 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Statistics Probabilities Econometrics Statistical Theory and Methods Probability Theory and Stochastic Processes Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Erscheint auch als Online-Ausgabe 10.1007/978-3-319-74380-6 978-3-319-74380-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030304326&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beran, Jan 1959- Mathematical foundations of time series analysis a concise introduction Statistics Probabilities Econometrics Statistical Theory and Methods Probability Theory and Stochastic Processes Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 |
| title | Mathematical foundations of time series analysis a concise introduction |
| title_auth | Mathematical foundations of time series analysis a concise introduction |
| title_exact_search | Mathematical foundations of time series analysis a concise introduction |
| title_full | Mathematical foundations of time series analysis a concise introduction Jan Beran |
| title_fullStr | Mathematical foundations of time series analysis a concise introduction Jan Beran |
| title_full_unstemmed | Mathematical foundations of time series analysis a concise introduction Jan Beran |
| title_short | Mathematical foundations of time series analysis |
| title_sort | mathematical foundations of time series analysis a concise introduction |
| title_sub | a concise introduction |
| topic | Statistics Probabilities Econometrics Statistical Theory and Methods Probability Theory and Stochastic Processes Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Statistics Probabilities Econometrics Statistical Theory and Methods Probability Theory and Stochastic Processes Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030304326&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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