Time series analysis: nonstationary and noninvertible distribution theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ, USA
Wiley
[2017]
|
| Edition: | Second edition |
| Series: | Wiley Series in Probability and Statistics
|
| Subjects: | |
| Online Access: | http://www.wiley-vch.de/publish/dt/books/ISBN978-1-119-13209-7/ Inhaltsverzeichnis |
| Physical Description: | xiv, 889 Seiten Diagramme |
| ISBN: | 9781119132097 1119132096 |
Staff View
MARC
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| 100 | 1 | |a Tanaka, Katsuto |d 1950- |e Verfasser |0 (DE-588)170068935 |4 aut | |
| 245 | 1 | 0 | |a Time series analysis |b nonstationary and noninvertible distribution theory |c Katsuto Tanaka |
| 250 | |a Second edition | ||
| 264 | 1 | |a Hoboken, NJ, USA |b Wiley |c [2017] | |
| 300 | |a xiv, 889 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley Series in Probability and Statistics | |
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| 653 | |a Econometric & Statistical Methods | ||
| 653 | |a Ökonometrie | ||
| 653 | |a Ökonometrie u. statistische Methoden | ||
| 653 | |a Probability & Mathematical Statistics | ||
| 653 | |a Statistics | ||
| 653 | |a Statistik | ||
| 653 | |a Time Series | ||
| 653 | |a Wahrscheinlichkeitsrechnung | ||
| 653 | |a Wahrscheinlichkeitsrechnung u. mathematische Statistik | ||
| 653 | |a Zeitreihen | ||
| 653 | |a Zeitreihenanalyse | ||
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Record in the Search Index
| _version_ | 1804177586840928256 |
|---|---|
| adam_text | Contents
Preface to the Second Edition xi
Preface to the First Edition xiii
Parti Analysis of Non Fractional Time Series I
1 Models for Nonstationarity and Noninvertibility 3
1.1 Statistics from the One-Dimensional Random Walk 3
1.1.1 Eigenvalue Approach 4
1.1.2 Stochastic Process Approach 11
1.1.3 The Fredholm Approach 12
1.1.4 An Overview of the Three Approaches 14
1.2 A Test Statistic from a Noninvertible Moving Average Model 16
1.3 The AR Unit Root Distribution 23
1.4 Various Statistics from the Two-Dimensional Random Walk 29
1.5 Statistics from the Cointegrated Process 41
1.6 Panel Unit Root Tests 47
2 Brownian Motion and Functional Central Limit
Theorems 51
2.1 The Space L2 of Stochastic Processes 51
2.2 The Brownian Motion 55
2.3 Mean Square Integration 58
2.3.1 The Mean Square Riemann Integral 59
2.3.2 The Mean Square Riemann—Stieltjes Integral 62
2.3.3 The Mean Square Ito Integral 66
2.4 The Ito Calculus 72
2.5 Weak Convergence of Stochastic Processes 77
2.6 The Functional Central Limit Theorem 81
2.7 FCLT for Linear Processes 87
2.8 FCLT for Martingale Differences 91
2.9 Weak Convergence to the Integrated Brownian Motion 99
vi I Contents
2.10 Weak Convergence to the Ornstein-Uhlenbeck Process 103
2.11 Weak Convergence of Vector-Valued Stochastic Processes 109
2.11.1 Space C* 109
2.11.2 Basic FCLT for Vector Processes 110
2.11.3 FCLT for Martingale Differences 112
2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion 115
2.12 Weak Convergence to the Ito Integral 118
3 The Stochastic Process Approach 127
3.1 Girsanov’s Theorem: O-U Processes 127
3.2 Girsanov’s Theorem: Integrated Brownian Motion 137
3.3 Girsanov’s Theorem: Vector-Valued Brownian Motion 142
3.4 The Cameron-Martin Formula 145
3.5 Advantages and Disadvantages of the Present Approach 147
4 The Fredholm Approach 149
4.1 Motivating Examples 149
4.2 The Fredholm Theory: The Homogeneous Case 155
4.3 The c.f. of the Quadratic Brownian Functional 161
4.4 Various Fredholm Determinants 171
4.5 The Fredholm Theory: The Nonhomogeneous Case 190
4.5.1 Computation of the Resolvent - Case 1 192
4.5.2 Computation of the Resolvent - Case 2 199
4.6 Weak Convergence of Quadratic Forms 203
5 Numerical Integration 213
5.1 Introduction 213
5.2 Numerical Integration: The Nonnegative Case 214
5.3 Numerical Integration: The Oscillating Case 220
5.4 Numerical Integration: The General Case 228
5.5 Computation of Percent Points 236
5.6 The Saddlepoint Approximation 240
6 Estimation Problems in Nonstationary Autoregressive
Models 245
6.1 Nonstationary Autoregressive Models 245
6.2 Convergence in Distribution of LSEs 250
6.2.1 Model A 251
6.2.2 Model В 253
6.2.3 Model C 255
6.2.4 Model D 257
6.3 The c.f.s for the Limiting Distributions of LSEs 260
6.3.1 The Fixed Initial Value Case 261
6.3.2 The Stationary Case 265
6.4 Tables and Figures of Limiting Distributions 267
6.5 Approximations to the Distributions of the LSEs 276
6.6 Nearly Nonstationary Seasonal AR Models 281
6.7 Continuous Record Asymptotics 289
6.8 Complex Roots on the Unit Circle 292
6.9 Autoregressive Models with Multiple Unit Roots 300
7 Estimation Problems in Noninvertible Moving Average
Models 311
7.1 Noninvertible Moving Average Models 311
7.2 The Local MLE in the Stationary Case 314
7.3 The Local MLE in the Conditional Case 325
7.4 Noninvertible Seasonal Models 330
7.4.1 The Stationary Case 331
7.4.2 The Conditional Case 333
7.4.3 Continuous Record Asymptotics 335
7.5 The Pseudolocal MLE 337
7.5.1 The Stationary Case 337
7.5.2 The Conditional Case 339
7.6 Probability of the Local MLE at Unity 341
1П The Relationship with the State Space Model 343
8 Unit Root Tests in Autoregressive Models 349
8.1 Introduction 349
8.2 Optimal Tests 350
8.2.1 The LBI Test 352
8.2.2 The LBIU Test 353
8.3 Equivalence of the LM Test with the LBI or LBIU Test 356
8.3.1 Equivalence with the LBI Test 356
8.3.2 Equivalence with the LBIU Test 358
8.4 Various Unit Root Tests 360
8.5 Integral Expressions for the Limiting Powers 362
8.5.1 Model A 363
8.5.2 Model В 364
8.5.3 Model C 365
8.5.4 Model D 367
8.6 Limiting Power Envelopes and Point Optimal Tests 369
8.7 Computation of the Limiting Powers 372
8.8 Seasonal Unit Root Tests 382
8.9 Unit Root Tests in the Dependent Case 389
8.10 The Unit Root Testing Problem Revisited 395
8.11 Unit Root Tests with Structural Breaks 398
8.12 Stochastic Trends Versus Deterministic Trends 402
8.12.1 Case of Integrated Processes 403
viii | Contents
Case of Near-Integrated Processes 406
Some Simulations 409
8.12.2
8.12.3
9
9.1
9.2
9.2.1
9.2.2
9.3
9.4
9.4.1
9.4.2
9.5
9.5.1
9.5.2
9.5.3
9.6
9.6.1
9.6.2
9.7
9.7.1
9.7.2
9.7.3
9.7.4
10
10.1
10.2
10.2.1
10.2.2
10.2.3
10.2.4
10.2.5
10.3
10.3.1
10.3.2
10.3.3
10.3.4
10.4
10.4.1
10.4.2
10.4.3
10.5
Unit Root Tests in Moving Average Models 41S
Introduction 415
The LBI and LBIU Tests 416
The Conditional Case 417
The Stationary Case 419
The Relationship with the Test Statistics in Differenced Form 424
Performance of the LBI and LBIU Tests 427
The Conditional Case 427
The Stationary Case 430
Seasonal Unit Root Tests 434
The Conditional Case 434
The Stationary Case 436
Power Properties 438
Unit Root Tests in the Dependent Case 444
The Conditional Case 444
The Stationary Case 446
The Relationship with Testing in the State Space Model 447
Case (I) 449
Case (II) 450
Case (III) 452
The Case of the Initial Value Known 454
Asymptotic Properties of Nonstationary Panel Unit Root
Tests 459
Introduction 459
Panel Autoregressive Models 461
Tests Based on the OLSE 463
Tests Based on the GLSE 471
Some Other Tests 475
Limiting Power Envelopes 480
Graphical Comparison 485
Panel Moving Average Models 488
Conditional Case 490
Stationary Case 494
Power Envelope 499
Graphical Comparison 502
Panel Stationarity Tests 507
Limiting Local Powers 508
Power Envelope 512
Graphical Comparison 514
Concluding Remarks 515
11 Statistical Analysis of Cointegration 517
11*1 Introduction 517
11.2 Case of No Cointegration 519
11.3 Cointegration Distributions: The Independent Case 524
11A Co integration Distributions: The Dependent Case 532
11.5 The Sampling Behavior of Cointegration Distributions 537
11.6 Testing for Cointegration 544
11.6.1 Tests for the Null of No Cointegration 544
11.6.2 Tests for the Null of Cointegration 547
11.7 Determination of the Cointegration Rank 552
11.8 Higher Order Cointegration 556
11.8.1 Cointegration in the 1(d) Case 556
11.8.2 Seasonal Cointegration 559
Part II Analysis of Fractional Time Series 567
12
12.1
12.1.1
12.1.2
12.2
12.2.1
12.2.2
12.3
12.3.1
12.3.2
12.4
12.5
12.6
12.7
12.7.1
12.7.2
12.7.3
12.8
12.8.1
12.8.2
12.8.3
12.8.3.1
12.8.3.2
12.8.3.3
12.8.3.4
ARFIMA Models and the Fractional Brownian Motion 569
Nonstationary Fractional Time Series 569
Case of d=- 570
2
Case of d 572
Testing for the Fractional Integration Order 575
1.1. d. Case 575
Dependent Case 581
Estimation for the Fractional Integration Order 584
1.1. d. Case 584
Dependent Case 586
Stationary Long-Memory Processes 591
The Fractional Brownian Motion 597
FCLT for Long-Memory Processes 603
Fractional Cointegration 608
Spurious Regression in the Fractional Case 609
Cointegrating Regression in the Fractional Case 610
Testing for Fractional Cointegration 614
The Wavelet Method for ARFIMA Models and the fBm 614
Basic Theory of the Wavelet Transform 615
Some Advantages of the Wavelet Transform 618
Some Applications of the Wavelet Analysis 625
Testing for d in ARFIMA Models 625
Testing for the Existence of Noise 626
Testing for Fractional Cointegration 627
Unit Root Tests 627
Contents
13 Statistical Inference Associated with the Fractional Brownian
Motion 629
13.1 Introduction 629
13.2 A Simple Continuous-Time Model Driven by the fBm 632
133 Quadratic Functionals of the Brownian Motion 641
13 A Derivation of the c.f. 645
13.4.1 Stochastic Process Approach via Girsanov’s Theorem 645
13.4.1.1 Case of H = 1/2 645
13.4.1.2 Case ofH 1/2 646
13.4.2 Fredholm Approach via the Fredholm Determinant 647
13.4.2.1 Case of// — 1/2 649
13.4.2.2 Case of H 1/2 650
13.5 Martingale Approximation to the fBm 651
13.6 The Fractional Unit Root Distribution 659
13.6.1 The FD Associated with the Approximate Distribution 659
13.6.2 An Interesting Moment Property 664
13.7 The Unit Root Test Under the fBm Error 669
14 Maximum Likelihood Estimation for the Fractional
Ornstein-Uhlenbeck Process 673
14.1 Introduction 673
14.2 Estimation of the Drift: Ergodic Case 677
14.2.1 Asymptotic Properties of the OLSEs 677
14.2.2 The MLE and MCE 679
14.3 Estimation of the Drift: Non-ergodic Case 687
14.3.1 Asymptotic Properties of the OLSE 687
14.3.2 The MLE 687
14.4 Estimation of the Drift: Boundary Case 692
14.4.1 Asymptotic Properties of the OLSEs 692
14.4.2 The MLE and MCE 693
14.5 Computation of Distributions and Moments of the MLE and
MCE 695
14.6 The MLE-based Unit Root Test Under the fBm Error 703
14.7 Concluding Remarks 707
15 Solutions to Problems 709
References 865
Author Index 879
Subject Index
883
|
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV044348166 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:50:26Z |
| institution | BVB |
| institution_GND | (DE-588)4101395-5 |
| isbn | 9781119132097 1119132096 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029751029 |
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| physical | xiv, 889 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | Wiley |
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| series2 | Wiley Series in Probability and Statistics |
| spelling | Tanaka, Katsuto 1950- Verfasser (DE-588)170068935 aut Time series analysis nonstationary and noninvertible distribution theory Katsuto Tanaka Second edition Hoboken, NJ, USA Wiley [2017] xiv, 889 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wiley Series in Probability and Statistics Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Econometric & Statistical Methods Ökonometrie Ökonometrie u. statistische Methoden Probability & Mathematical Statistics Statistics Statistik Time Series Wahrscheinlichkeitsrechnung Wahrscheinlichkeitsrechnung u. mathematische Statistik Zeitreihen Zeitreihenanalyse Zeitreihenanalyse (DE-588)4067486-1 s DE-604 John Wiley and Sons (DE-588)4101395-5 pbl Erscheint auch als Online-Ausgabe PDF 9781119132110 Erscheint auch als Online-Ausgabe epub 9781119132134 X:MVB http://www.wiley-vch.de/publish/dt/books/ISBN978-1-119-13209-7/ 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=029751029&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tanaka, Katsuto 1950- Time series analysis nonstationary and noninvertible distribution theory Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 |
| title | Time series analysis nonstationary and noninvertible distribution theory |
| title_auth | Time series analysis nonstationary and noninvertible distribution theory |
| title_exact_search | Time series analysis nonstationary and noninvertible distribution theory |
| title_full | Time series analysis nonstationary and noninvertible distribution theory Katsuto Tanaka |
| title_fullStr | Time series analysis nonstationary and noninvertible distribution theory Katsuto Tanaka |
| title_full_unstemmed | Time series analysis nonstationary and noninvertible distribution theory Katsuto Tanaka |
| title_short | Time series analysis |
| title_sort | time series analysis nonstationary and noninvertible distribution theory |
| title_sub | nonstationary and noninvertible distribution theory |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Zeitreihenanalyse |
| url | http://www.wiley-vch.de/publish/dt/books/ISBN978-1-119-13209-7/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029751029&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tanakakatsuto timeseriesanalysisnonstationaryandnoninvertibledistributiontheory AT johnwileyandsons timeseriesanalysisnonstationaryandnoninvertibledistributiontheory |