Stochastic models for time series:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2018]
|
| Schriftenreihe: | Mathématiques et applications
80 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | xx, 308 Seiten Illustrationen 23.5 cm x 15.5 cm |
| ISBN: | 9783319769370 3319769375 |
Internformat
MARC
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| 100 | 1 | |a Doukhan, Paul |d 1955- |0 (DE-588)11369363X |4 aut | |
| 245 | 1 | 0 | |a Stochastic models for time series |c Paul Doukhan |
| 264 | 1 | |a Cham |b Springer |c [2018] | |
| 264 | 4 | |c © 2018 | |
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| 653 | |a PBT | ||
| 653 | |a KCH | ||
| 653 | |a Non-linear time series | ||
| 653 | |a Integer valued models | ||
| 653 | |a Markov chains | ||
| 653 | |a Stochastic processes | ||
| 653 | |a Gaussian Convergence | ||
| 653 | |a Spectral estimation | ||
| 653 | |a Memory models | ||
| 653 | |a LARCH-type models | ||
| 653 | |a Weak dependence conditions | ||
| 653 | |a Functional estimation | ||
| 653 | |a Bootstrap | ||
| 653 | |a Non-Markove linear models | ||
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Datensatz im Suchindex
| _version_ | 1804179021948256256 |
|---|---|
| adam_text | Contents
Part I Independence and Stationarity
1 Independence........................................................... 3
2 Gaussian Convergence and Inequalities.................................. 9
2.1 Gaussian Convergence............................................ 9
2.1.1 Central Limit Theorem.................................. 12
2.1.2 Empirical Median....................................... 13
2.1.3 Gaussian Approximation for Binomials................... 14
2.2 Quantitative Results........................................... 17
2.2.1 Moment Inequalities.................................... 17
2.2.2 Exponential Inequalities............................... 22
3 Estimation Concepts................................................... 27
3.1 Empirical Estimators........................................... 27
3.2 Contrasts...................................................... 30
3.3 Functional Estimation.......................................... 31
3.4 Division Trick ............................................... 41
3.5 A Semi-parametric Test......................................... 45
4 Stationarity.......................................................... 49
4.1 Stationarity................................................... 49
4.2 Spectral Representation........................................ 53
4.3 Range and Spectral Density..................................... 59
4.3.1 Limit Variance......................................... 63
4.3.2 Cramer-Wold Representation............................. 64
4.4 Spectral Estimation............................................ 65
4.4.1 Functional Spectral Estimation........................ 66
4.4.2 Whittle Estimation..................................... 67
4.5 Parametric Estimation.......................................... 67
4.6 Subsampling.................................................... 69
xv
XVI
Contents
Part II Models of Time Series
5 Gaussian Chaos................................................... ^3
5.1 Gaussian Processes.......................................... 73
5.1.1 Fractional Brownian Motion.......................... 74
5.2 Gaussian Chaos.............................................. 78
5.2.1 Hermite Polynomials............................... 80
5.2.2 Second Order Moments................................ 86
5.2.3 Higher Order Moments................................ 90
5.2.4 Integral Representation of the Brownian Chaos....... 94
5.2.5 The Fourth Order Moment Method...................... 96
6 Linear Processes.................................................. 101
6.1 Stationary Linear Models.................................. 101
6.2 ARMA(p, ?)-Processes..................................... 104
6.3 Yule-Walker Equations..................................... 107
6.4 ARFIMA(0,d,0)-Processes.................................... 108
6.5 ARFTMA(p,d, ^-Processes......... ......................... 112
6.6 Extensions ................................................ 113
7 Non-linear Processes............................................. 115
7.1 Discrete Chaos............................................ 115
7.1.1 Volterra Expansions............................... 115
7.1.2 Appell Polynomials................................ 117
7.2 Memory Models............................................. 120
7.2.1 Bilinear Models.................................... 122
7.2.2 LARCH (oo) -Models................................. 127
7.3 Stable Markov Chains...................................... 128
7.3.1 AR-ARCH-Models..................................... 131
7.3.2 Moments of ARCH(l)-Models.......................... 133
7.3.3 Estimation of LARCH(l)-Models...................... 135
7.3.4 Branching Models.................................. 144
7.3.5 Integer Valued Autoregressions..................... 147
7.3.6 Generalized Linear Models ......................... 149
7.3.7 Non-linear AR(d)-Models............................ 154
7.4 Bernoulli Schemes.......................................... 155
7.4.1 Structure and Tools................................ 155
7.4.2 Couplings . . ..................................... 162
8 Associated Processes........................................... 167
8.1 Association................................................ 167
8.2 Associated Processes....................................... 169
8.3 Main Inequality............................................ 170
8.4 Limit Theory............................................... 172
Contents xvii
Part III Dependence
9 Dependence...................................................... 177
9.1 Ergodic Theorem.......................................... 177
9.2 Range.................................................... 186
10 Long-Range Dependence........................................... 189
10.1 Gaussian Processes....................................... 189
10.2 Gaussian Polynomials..................................... 191
10.3 Rosenblatt Process....................................... 192
10.4 Linear Processes......................................... 195
10.5 Functions of Linear Processes............................ 196
10.6 More LRD Models.......................................... 198
10.6.1 Integer Valued Trawl Models....................... 198
10.6.2 LARCH-Models...................................... 201
10.6.3 Randomly Fractional Differences................... 202
10.6.4 Perturbed Linear Models........................... 203
10.6.5 Non-linear Bemoulli-Shift Models.................. 203
11 Short-Range Dependence.......................................... 205
11.1 Weak-Dependence.......................................... 205
11.2 Strong Mixing............................................ 206
11.3 Bootstrapping AR(l)-Models............................... 209
11.4 Weak-Dependence Conditions.............................. 211
11.5 Proving Limit Theorems................................... 219
12 Moments and Cumulants........................................... 225
12.1 Method of Moments....................................... 226
12.1.1 Notations......................................... 226
12.1.2 Combinatorics of Moments.......................... 228
12.2 Dependence and Cumulants................................. 230
12.2.1 More Dependence Coefficients...................... 231
12.2.2 Sums of Cumulants................................. 235
12.2.3 Moments of Sums................................... 236
12.2.4 Rosenthal’s Inequality............................ 238
12.3 Dependent Kernel Density Estimation...................... 240
Erratum to: Non-linear Processes..................................... El
Appendix A: Probability and Distributions........................... 247
Appendix B: Convergence and Processes............................... 275
Appendix C: R Scripts Used for the Figures.......................... 287
References.......................................................... 301
Index............................................................... 305
|
| any_adam_object | 1 |
| author | Doukhan, Paul 1955- |
| author_GND | (DE-588)11369363X |
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| author_sort | Doukhan, Paul 1955- |
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| bvnumber | BV045263872 |
| classification_rvk | QH 237 |
| ctrlnum | (OCoLC)1077591821 (DE-599)DNB1151589667 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| spelling | Doukhan, Paul 1955- (DE-588)11369363X aut Stochastic models for time series Paul Doukhan Cham Springer [2018] © 2018 xx, 308 Seiten Illustrationen 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Mathématiques et applications 80 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf PBT KCH Non-linear time series Integer valued models Markov chains Stochastic processes Gaussian Convergence Spectral estimation Memory models LARCH-type models Weak dependence conditions Functional estimation Bootstrap Non-Markove linear models Stochastischer Prozess (DE-588)4057630-9 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Springer International Publishing (DE-588)1064344704 pbl Elektronische Reproduktion 9783319769387 Erscheint auch als Online-Ausgabe 978-3-319-76938-7 Mathématiques et applications 80 (DE-604)BV006642035 80 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=63cc4a1681a345688deec68f8e555141&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ 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=030651761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doukhan, Paul 1955- Stochastic models for time series Mathématiques et applications Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4057630-9 |
| title | Stochastic models for time series |
| title_auth | Stochastic models for time series |
| title_exact_search | Stochastic models for time series |
| title_full | Stochastic models for time series Paul Doukhan |
| title_fullStr | Stochastic models for time series Paul Doukhan |
| title_full_unstemmed | Stochastic models for time series Paul Doukhan |
| title_short | Stochastic models for time series |
| title_sort | stochastic models for time series |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Zeitreihenanalyse Stochastischer Prozess |
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