Large sample inference for long memory processes:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
London
ICP
2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 577 S. graph. Darst. |
| ISBN: | 9781848162785 1848162782 |
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| 245 | 1 | 0 | |a Large sample inference for long memory processes |c Liudas Giraitis ; Hira I. Koul ; Donatas Surgailis |
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Record in the Search Index
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| adam_text | Titel: Large sample inference for long memory processes
Autor: Giraitis, Liudas
Jahr: 2012
Contents
Preface v
Notation and Conventions xv
1. Introduction 1
2. Some Preliminaries 7
2.1 Preliminaries from trigonometry.............. 7
2.2 Stationarity, spectral density, and autocovariance..... 9
2.3 Slowly and regulaxly varying functions........... 18
2.4 Hermite and Appell polynomials.............. 22
2.5 Miscellaneous preliminaries................. 29
3. Long Memory Processes 33
3.1 Characterization of short and long memory processes . . . 33
3.2 Wold decomposition and linear processes.......... 38
3.3 Asymptotics of the variance................. 42
3.4 Self-similarity, long memory, and fractional Brownian
motion............................. 45
3.5 Other classes of long memory processes .......... 52
4. Limit Theory for Sums 55
4.1 Introduction.......................... 55
4.2 Cumulant criterion for CLT................. 56
4.3 CLT for sums of a linear process.............. 62
x Large Sample Inference for Long Memory Processes
4.4 Partial-sum process...................... 73
4.5 More results for weighted sums............... 80
4.6 Sums of a transformed Gaussian process.......... 88
4.7 Non-central limit theorems ................. 101
4.8 Limit theorems for polynomial forms............ 107
5. Properties of the DFT and the Periodogram 111
5.1 Introduction.......................... 111
5.2 Covariances of the DFT................... 112
5.3 Some other properties of the DFT and the
periodogram.......................... 123
6. Asymptotic Theory for Quadratic Forms 132
6.1 Introduction.......................... 132
6.2 Asymptotic normality for sums of weighted
periodograms......................... 133
6.3 Asymptotic normality of quadratic forms ......... 157
6.3.1 Stronger sufficient conditions for asymptotic
normality....................... 168
7. Parametric Models 174
7.1 Introduction.......................... 174
7.2 ARFIMA modeis....................... 174
7.3 GARMA modeis....................... 185
7.4 Simulation of ARFIMA processes.............. 191
7.5 Aggregation, disaggregation, and long memory...... 197
8. Estimation 202
8.1 Introduction.......................... 202
8.2 Parametric model: consistency............... 204
8.3 Parametric model: asymptotic normality.......... 213
8.3.1 Parametric modeis: asymptotic normality of
Whittle estimators.................. 213
8.3.2 Whittle estimators in ARFIMA modeis...... 219
8.4 Semiparametric modeis ................... 221
Contents xi
8.4.1 R/S estimation method............... 222
8.4.2 Log-periodogram estimator............. 225
8.5 Local Whittle estimators................... 226
8.5.1 Semiparametric modeis: consistency of local
Whittle estimators.................. 229
8.5.2 Local Whittle estimators for linear processes . . . 240
8.6 Signal plus noise processes.................. 245
8.6.1 Estimation in signal+noise............. 246
8.6.2 Application to a stochastic volatility model .... 255
8.7 Monte Carlo experiment................... 258
9. Elementary Inference Problems 265
9.1 Introduction.......................... 265
9.2 Linear-trend model...................... 266
9.3 Estimation of the mean p.................. 272
9.4 Estimation of the long-run variance............. 275
9.5 Testing for long memory and breaks............ 285
10. Empirical Processes 305
10.1 Introduction.......................... 305
10.2 Uniform reduction principle................. 307
10.2.1 URP: Gaussian case................. 308
10.2.2 URP: moving-average case............. 314
10.3 Expansion of the empiricals................. 328
10.3.1 Expansion of empiricals: Gaussian case...... 329
10.3.2 Expansion of empiricals: moving-average case . . 336
11. Regression Models 352
11.1 Introduction.......................... 352
11.2 First-order asymptotics of M and R estimators...... 354
11.2.1 CLT for the LS estimator.............. 359
11.2.2 First-order asymptotics of M estimators...... 361
11.2.3 First-order asymptotics of R estimators...... 369
11.3 Higher-order asymptotics of M estimators......... 376
11.4 Whittle estimator in linear regression. ........... 382
xii Large Sample Inference for Long Memory Processes
11.5 Non-linear regression with random design......... 394
11.6 A Simulation study...................... 412
12. Non-parametric Regression 415
12.1 Introduction.......................... 415
12.2 Uniform design........................ 415
12.2.1 Some preliminaries for p.............. 417
12.2.2 Asymptotic properties of p............. 424
12.2.3 Uniform rate of convergence............ 425
12.3 Asymptotics of a2 ...................... 429
12.3.1 Some preliminaries for a1.............. 430
12.3.2 MSE and asymptotic distribution of a2...... 437
12.4 Estimation of Var(/t(x))................... 439
13. Model Diagnostics 446
13.1 Introduction.......................... 446
13.2 Lack-of-fit tests........................ 447
13.2.1 Testing for Hq: martingale-difference errors .... 449
13.2.2 Lack-of-fit tests: LM moving-average errors .... 455
13.3 Long memory design and heteroscedastic errors...... 464
13.3.1 Lack-of-fit tests: heteroscedastic LMMA errors . . 476
13.3.2 A Monte Carlo Simulation............. 479
13.3.3 Application to the forward premium anomaly . . 482
13.3.4 Application to a foreign exchange data set .... 484
13.4 Testing a subhypothesis................... 488
13.4.1 Random design ................... 490
13.4.2 Non-random design................. 501
13.5 Goodness-of-fit of a marginal distribution function .... 505
14. Appendix 519
14.1 Appell polynomials, Wick products, and diagram
formulas............................ 519
14.2 Sums of Appell polynomials................. 528
14.3 Multiple Wiener-Ito integrals................ 531
14.4 Limit of traces of Toeplitz matrices............. 545
Contents
15. Bibliography 554
Author Index 571
Subject Index 575
|
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| author | Giraitis, Liudas Koul, Hira L. Surgailis, Donatas |
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| isbn | 9781848162785 1848162782 |
| language | English |
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| physical | XVI, 577 S. graph. Darst. |
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| spelling | Giraitis, Liudas Verfasser (DE-588)17162839X aut Large sample inference for long memory processes Liudas Giraitis ; Hira I. Koul ; Donatas Surgailis London ICP 2012 XVI, 577 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stichprobenumfang (DE-588)4183251-6 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Long-memory-Prozess (DE-588)4345167-6 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 s Long-memory-Prozess (DE-588)4345167-6 s Stichprobenumfang (DE-588)4183251-6 s DE-604 Koul, Hira L. Verfasser (DE-588)170612511 aut Surgailis, Donatas Verfasser (DE-588)171791738 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020767978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Giraitis, Liudas Koul, Hira L. Surgailis, Donatas Large sample inference for long memory processes Stichprobenumfang (DE-588)4183251-6 gnd Statistische Schlussweise (DE-588)4182963-3 gnd Long-memory-Prozess (DE-588)4345167-6 gnd |
| subject_GND | (DE-588)4183251-6 (DE-588)4182963-3 (DE-588)4345167-6 |
| title | Large sample inference for long memory processes |
| title_auth | Large sample inference for long memory processes |
| title_exact_search | Large sample inference for long memory processes |
| title_full | Large sample inference for long memory processes Liudas Giraitis ; Hira I. Koul ; Donatas Surgailis |
| title_fullStr | Large sample inference for long memory processes Liudas Giraitis ; Hira I. Koul ; Donatas Surgailis |
| title_full_unstemmed | Large sample inference for long memory processes Liudas Giraitis ; Hira I. Koul ; Donatas Surgailis |
| title_short | Large sample inference for long memory processes |
| title_sort | large sample inference for long memory processes |
| topic | Stichprobenumfang (DE-588)4183251-6 gnd Statistische Schlussweise (DE-588)4182963-3 gnd Long-memory-Prozess (DE-588)4345167-6 gnd |
| topic_facet | Stichprobenumfang Statistische Schlussweise Long-memory-Prozess |
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