Time series analysis: nonstationary and noninvertible distribution theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Chichester, West Sussex
Wiley
[2017]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | FRO01 TUM01 UBG01 UBT01 UPA01 URL des Erstveröffentlichers Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes Cover; Title Page; Copyright; Contents; Preface to the Second Edition; Preface to the First Edition; Part I Analysis of Non Fractional Time Series; Chapter 1 Models for Nonstationarity and Noninvertibility; 1.1 Statistics from the One-Dimensional Random Walk; 1.1.1 Eigenvalue Approach; 1.1.2 Stochastic Process Approach; 1.1.3 The Fredholm Approach; 1.1.4 An Overview of the Three Approaches; 1.2 A Test Statistic from a Noninvertible Moving Average Model; 1.3 The AR Unit Root Distribution; 1.4 Various Statistics from the Two-Dimensional Random Walk; 1.5 Statistics from the Cointegrated Process 1.6 Panel Unit Root TestsChapter 2 Brownian Motion and Functional Central Limit Theorems; 2.1 The Space L2 of Stochastic Processes; 2.2 The Brownian Motion; 2.3 Mean Square Integration; 2.3.1 The Mean Square Riemann Integral; 2.3.2 The Mean Square Riemann-Stieltjes Integral; 2.3.3 The Mean Square Ito Integral; 2.4 The Ito Calculus; 2.5 Weak Convergence of Stochastic Processes; 2.6 The Functional Central Limit Theorem; 2.7 FCLT for Linear Processes; 2.8 FCLT for Martingale Differences; 2.9 Weak Convergence to the Integrated Brownian Motion 2.10 Weak Convergence to the Ornstein-Uhlenbeck Process2.11 Weak Convergence of Vector-Valued Stochastic Processes; 2.11.1 Space Cq; 2.11.2 Basic FCLT for Vector Processes; 2.11.3 FCLT for Martingale Differences; 2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion; 2.12 Weak Convergence to the Ito Integral; Chapter 3 The Stochastic Process Approach; 3.1 Girsanov's Theorem: O-U Processes; 3.2 Girsanov's Theorem: Integrated Brownian Motion; 3.3 Girsanov's Theorem: Vector-Valued Brownian Motion; 3.4 The Cameron-Martin Formula; 3.5 Advantages and Disadvantages of the Present Approach Chapter 4 The Fredholm Approach4.1 Motivating Examples; 4.2 The Fredholm Theory: The Homogeneous Case; 4.3 The c.f. of the Quadratic Brownian Functional; 4.4 Various Fredholm Determinants; 4.5 The Fredholm Theory: The Nonhomogeneous Case; 4.5.1 Computation of the Resolvent-Case 1; 4.5.2 Computation of the Resolvent-Case 2; 4.6 Weak Convergence of Quadratic Forms; Chapter 5 Numerical Integration; 5.1 Introduction; 5.2 Numerical Integration: The Nonnegative Case; 5.3 Numerical Integration: The Oscillating Case; 5.4 Numerical Integration: The General Case; 5.5 Computation of Percent Points 5.6 The Saddlepoint ApproximationChapter 6 Estimation Problems in Nonstationary Autoregressive Models; 6.1 Nonstationary Autoregressive Models; 6.2 Convergence in Distribution of LSEs; 6.2.1 Model A; 6.2.2 Model B; 6.2.3 Model C; 6.2.4 Model D; 6.3 The c.f.s for the Limiting Distributions of LSEs; 6.3.1 The Fixed Initial Value Case; 6.3.2 The Stationary Case; 6.4 Tables and Figures of Limiting Distributions; 6.5 Approximations to the Distributions of the LSEs; 6.6 Nearly Nonstationary Seasonal AR Models; 6.7 Continuous Record Asymptotics; 6.8 Complex Roots on the Unit Circle |
| Beschreibung: | 1 online resource |
| ISBN: | 9781119132165 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV044304301 | ||
| 003 | DE-604 | ||
| 005 | 20200309 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 170510s2017 |||| o||u| ||||||eng d | ||
| 020 | |a 9781119132165 |9 978-1-119-13216-5 | ||
| 024 | 7 | |a 10.1002/9781119132165 |2 doi | |
| 035 | |a (OCoLC)992514180 | ||
| 035 | |a (DE-599)BVBBV044304301 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-861 |a DE-703 |a DE-739 |a DE-91 | ||
| 084 | |a QH 237 |0 (DE-625)141552: |2 rvk | ||
| 084 | |a SK 845 |0 (DE-625)143262: |2 rvk | ||
| 084 | |a MAT 634f |2 stub | ||
| 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 Chichester, West Sussex |b Wiley |c [2017] | |
| 300 | |a 1 online resource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Includes bibliographical references and indexes | ||
| 500 | |a Cover; Title Page; Copyright; Contents; Preface to the Second Edition; Preface to the First Edition; Part I Analysis of Non Fractional Time Series; Chapter 1 Models for Nonstationarity and Noninvertibility; 1.1 Statistics from the One-Dimensional Random Walk; 1.1.1 Eigenvalue Approach; 1.1.2 Stochastic Process Approach; 1.1.3 The Fredholm Approach; 1.1.4 An Overview of the Three Approaches; 1.2 A Test Statistic from a Noninvertible Moving Average Model; 1.3 The AR Unit Root Distribution; 1.4 Various Statistics from the Two-Dimensional Random Walk; 1.5 Statistics from the Cointegrated Process | ||
| 500 | |a 1.6 Panel Unit Root TestsChapter 2 Brownian Motion and Functional Central Limit Theorems; 2.1 The Space L2 of Stochastic Processes; 2.2 The Brownian Motion; 2.3 Mean Square Integration; 2.3.1 The Mean Square Riemann Integral; 2.3.2 The Mean Square Riemann-Stieltjes Integral; 2.3.3 The Mean Square Ito Integral; 2.4 The Ito Calculus; 2.5 Weak Convergence of Stochastic Processes; 2.6 The Functional Central Limit Theorem; 2.7 FCLT for Linear Processes; 2.8 FCLT for Martingale Differences; 2.9 Weak Convergence to the Integrated Brownian Motion | ||
| 500 | |a 2.10 Weak Convergence to the Ornstein-Uhlenbeck Process2.11 Weak Convergence of Vector-Valued Stochastic Processes; 2.11.1 Space Cq; 2.11.2 Basic FCLT for Vector Processes; 2.11.3 FCLT for Martingale Differences; 2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion; 2.12 Weak Convergence to the Ito Integral; Chapter 3 The Stochastic Process Approach; 3.1 Girsanov's Theorem: O-U Processes; 3.2 Girsanov's Theorem: Integrated Brownian Motion; 3.3 Girsanov's Theorem: Vector-Valued Brownian Motion; 3.4 The Cameron-Martin Formula; 3.5 Advantages and Disadvantages of the Present Approach | ||
| 500 | |a Chapter 4 The Fredholm Approach4.1 Motivating Examples; 4.2 The Fredholm Theory: The Homogeneous Case; 4.3 The c.f. of the Quadratic Brownian Functional; 4.4 Various Fredholm Determinants; 4.5 The Fredholm Theory: The Nonhomogeneous Case; 4.5.1 Computation of the Resolvent-Case 1; 4.5.2 Computation of the Resolvent-Case 2; 4.6 Weak Convergence of Quadratic Forms; Chapter 5 Numerical Integration; 5.1 Introduction; 5.2 Numerical Integration: The Nonnegative Case; 5.3 Numerical Integration: The Oscillating Case; 5.4 Numerical Integration: The General Case; 5.5 Computation of Percent Points | ||
| 500 | |a 5.6 The Saddlepoint ApproximationChapter 6 Estimation Problems in Nonstationary Autoregressive Models; 6.1 Nonstationary Autoregressive Models; 6.2 Convergence in Distribution of LSEs; 6.2.1 Model A; 6.2.2 Model B; 6.2.3 Model C; 6.2.4 Model D; 6.3 The c.f.s for the Limiting Distributions of LSEs; 6.3.1 The Fixed Initial Value Case; 6.3.2 The Stationary Case; 6.4 Tables and Figures of Limiting Distributions; 6.5 Approximations to the Distributions of the LSEs; 6.6 Nearly Nonstationary Seasonal AR Models; 6.7 Continuous Record Asymptotics; 6.8 Complex Roots on the Unit Circle | ||
| 650 | 7 | |a Time-series analysis |2 fast | |
| 650 | 7 | |a MATHEMATICS / Applied |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 4 | |a Time-series analysis | |
| 650 | 0 | 7 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-1-119-13209-7 |
| 856 | 4 | 0 | |u https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029708109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 912 | |a ZDB-35-WIC | ||
| 940 | 1 | |q UBG_PDA_WIC | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029708109 | ||
| 966 | e | |u https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 |l FRO01 |p ZDB-35-WIC |q FRO_PDA_WIC |x Verlag |3 Volltext | |
| 966 | e | |u https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 |l TUM01 |p ZDB-35-WIC |q TUM_Einzelkauf |x Verlag |3 Volltext | |
| 966 | e | |u https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 |l UBG01 |p ZDB-35-WIC |q UBG_PDA_WIC |x Verlag |3 Volltext | |
| 966 | e | |u https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 |l UBT01 |p ZDB-35-WIC |q UBT_PDA_WIC_Kauf |x Verlag |3 Volltext | |
| 966 | e | |u https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 |l UPA01 |p ZDB-35-WIC |q UPA_PDA_WIC_Kauf |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804177511612940288 |
|---|---|
| adam_text | Titel: Time series analysis
Autor: Tanaka, Katsuto
Jahr: 2017
Contents
Preface to the Second Edition xi
Preface to the First Edition xiii
Part I Analysis of Non Fractional Time Series 1
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 1 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 С4 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 Ð’ 253
6.2.3 Model С 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
Contents j vii
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
171 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 Ð’ 364
8.5.3 Model С 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
X j 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
13.3 Quadratic Functionals of the Brownian Motion 641
13.4 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 of Я 1/2 646
13.4.2 Fredholm Approach via the Fredholm Determinant 647
13.4.2.1 Case of Я = 1/2 649
13.4.2.2 Case of Я 1/2 650
13.5 Martingale Approximation to the fBm 651
13.6 Ihe 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 365
Author Index 879
Subject Index 883
Contents ix
11 Statistical Analysis of Cointegration 517
11.1 Introduction S17
11.2 Case of No Cointegration 519
11.3 Cointegration Distributions: The Independent Case 524
11.4 Cointegration 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 {d) Case 556
11.8.2 Seasonal Cointegration 559
Partii Analysis of Fractional Time Series 567
12 ARFIMA Models and the Fractional Brownian Motion 569
12.1 Nonstationary Fractional Time Series 569
12.1.1 Case of d =- 570
?
12.1.2 Case oÃd â– â– 572
2
12.2 Testing for the Fractional Integration Order 575
12.2.1 i.i.d. Case 575
12.2.2 Dependent Case 581
12.3 Estimation for the Fractional Integration Order 584
12.3.1 i.i.d. Case 584
12.3.2 Dependent Case 586
12.4 Stationary Long-Memory Processes 591
12.5 The Fractional Brownian Motion 597
12.6 FCLT for Long-Memory Processes 603
12.7 Fractional Cointegration 608
12.7.1 Spurious Regression in the Fractional Case 609
12.7.2 Cointegrating Regression in the Fractional Case 610
12.7.3 Testing for Fractional Cointegration 614
12.8 The Wavelet Method for ARFIMA Models and the fBm 614
12.8.1 Basic Theory of the Wavelet Transform 615
12.8.2 Some Advantages of the Wavelet Transform 618
12.8.3 Some Applications of the Wavelet Analysis 625
12.8.3.1 Testing for if in ARFIMA Models 625
12.8.3.2 Testing for the Existence of Noise 626
12.8.3.3 Testing for Fractional Cointegration 627
12.8.3.4 Unit Root Tests 627
X j 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
13.3 Quadratic Functionals of the Brownian Motion 641
13.4 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 of Я 1/2 646
13.4.2 Fredholm Approach via the Fredholm Determinant 647
13.4.2.1 Case of Я = 1/2 649
13.4.2.2 Case of Я 1/2 650
13.5 Martingale Approximation to the fBm 651
13.6 Ihe 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 365
Author Index 879
Subject Index 883
|
| any_adam_object | 1 |
| author | Tanaka, Katsuto 1950- |
| author_GND | (DE-588)170068935 |
| author_facet | Tanaka, Katsuto 1950- |
| author_role | aut |
| author_sort | Tanaka, Katsuto 1950- |
| author_variant | k t kt |
| building | Verbundindex |
| bvnumber | BV044304301 |
| classification_rvk | QH 237 SK 845 |
| classification_tum | MAT 634f |
| collection | ZDB-35-WIC |
| ctrlnum | (OCoLC)992514180 (DE-599)BVBBV044304301 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Second edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05628nmm a2200601zc 4500</leader><controlfield tag="001">BV044304301</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200309 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">170510s2017 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781119132165</subfield><subfield code="9">978-1-119-13216-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1002/9781119132165</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)992514180</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044304301</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-861</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-91</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 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">Tanaka, Katsuto</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)170068935</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Time series analysis</subfield><subfield code="b">nonstationary and noninvertible distribution theory</subfield><subfield code="c">Katsuto Tanaka</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Chichester, West Sussex</subfield><subfield code="b">Wiley</subfield><subfield code="c">[2017]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Wiley series in probability and statistics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and indexes</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Cover; Title Page; Copyright; Contents; Preface to the Second Edition; Preface to the First Edition; Part I Analysis of Non Fractional Time Series; Chapter 1 Models for Nonstationarity and Noninvertibility; 1.1 Statistics from the One-Dimensional Random Walk; 1.1.1 Eigenvalue Approach; 1.1.2 Stochastic Process Approach; 1.1.3 The Fredholm Approach; 1.1.4 An Overview of the Three Approaches; 1.2 A Test Statistic from a Noninvertible Moving Average Model; 1.3 The AR Unit Root Distribution; 1.4 Various Statistics from the Two-Dimensional Random Walk; 1.5 Statistics from the Cointegrated Process</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">1.6 Panel Unit Root TestsChapter 2 Brownian Motion and Functional Central Limit Theorems; 2.1 The Space L2 of Stochastic Processes; 2.2 The Brownian Motion; 2.3 Mean Square Integration; 2.3.1 The Mean Square Riemann Integral; 2.3.2 The Mean Square Riemann-Stieltjes Integral; 2.3.3 The Mean Square Ito Integral; 2.4 The Ito Calculus; 2.5 Weak Convergence of Stochastic Processes; 2.6 The Functional Central Limit Theorem; 2.7 FCLT for Linear Processes; 2.8 FCLT for Martingale Differences; 2.9 Weak Convergence to the Integrated Brownian Motion</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">2.10 Weak Convergence to the Ornstein-Uhlenbeck Process2.11 Weak Convergence of Vector-Valued Stochastic Processes; 2.11.1 Space Cq; 2.11.2 Basic FCLT for Vector Processes; 2.11.3 FCLT for Martingale Differences; 2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion; 2.12 Weak Convergence to the Ito Integral; Chapter 3 The Stochastic Process Approach; 3.1 Girsanov's Theorem: O-U Processes; 3.2 Girsanov's Theorem: Integrated Brownian Motion; 3.3 Girsanov's Theorem: Vector-Valued Brownian Motion; 3.4 The Cameron-Martin Formula; 3.5 Advantages and Disadvantages of the Present Approach</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Chapter 4 The Fredholm Approach4.1 Motivating Examples; 4.2 The Fredholm Theory: The Homogeneous Case; 4.3 The c.f. of the Quadratic Brownian Functional; 4.4 Various Fredholm Determinants; 4.5 The Fredholm Theory: The Nonhomogeneous Case; 4.5.1 Computation of the Resolvent-Case 1; 4.5.2 Computation of the Resolvent-Case 2; 4.6 Weak Convergence of Quadratic Forms; Chapter 5 Numerical Integration; 5.1 Introduction; 5.2 Numerical Integration: The Nonnegative Case; 5.3 Numerical Integration: The Oscillating Case; 5.4 Numerical Integration: The General Case; 5.5 Computation of Percent Points</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">5.6 The Saddlepoint ApproximationChapter 6 Estimation Problems in Nonstationary Autoregressive Models; 6.1 Nonstationary Autoregressive Models; 6.2 Convergence in Distribution of LSEs; 6.2.1 Model A; 6.2.2 Model B; 6.2.3 Model C; 6.2.4 Model D; 6.3 The c.f.s for the Limiting Distributions of LSEs; 6.3.1 The Fixed Initial Value Case; 6.3.2 The Stationary Case; 6.4 Tables and Figures of Limiting Distributions; 6.5 Approximations to the Distributions of the LSEs; 6.6 Nearly Nonstationary Seasonal AR Models; 6.7 Continuous Record Asymptotics; 6.8 Complex Roots on the Unit Circle</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Time-series analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Applied</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Probability & Statistics / General</subfield><subfield code="2">bisacsh</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="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="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-1-119-13209-7</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029708109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-35-WIC</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">UBG_PDA_WIC</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029708109</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165</subfield><subfield code="l">FRO01</subfield><subfield code="p">ZDB-35-WIC</subfield><subfield code="q">FRO_PDA_WIC</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165</subfield><subfield code="l">TUM01</subfield><subfield code="p">ZDB-35-WIC</subfield><subfield code="q">TUM_Einzelkauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165</subfield><subfield code="l">UBG01</subfield><subfield code="p">ZDB-35-WIC</subfield><subfield code="q">UBG_PDA_WIC</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165</subfield><subfield code="l">UBT01</subfield><subfield code="p">ZDB-35-WIC</subfield><subfield code="q">UBT_PDA_WIC_Kauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-35-WIC</subfield><subfield code="q">UPA_PDA_WIC_Kauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV044304301 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:49:15Z |
| institution | BVB |
| isbn | 9781119132165 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029708109 |
| oclc_num | 992514180 |
| open_access_boolean | |
| owner | DE-861 DE-703 DE-739 DE-91 DE-BY-TUM |
| owner_facet | DE-861 DE-703 DE-739 DE-91 DE-BY-TUM |
| physical | 1 online resource |
| psigel | ZDB-35-WIC UBG_PDA_WIC ZDB-35-WIC FRO_PDA_WIC ZDB-35-WIC TUM_Einzelkauf ZDB-35-WIC UBG_PDA_WIC ZDB-35-WIC UBT_PDA_WIC_Kauf ZDB-35-WIC UPA_PDA_WIC_Kauf |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Wiley |
| record_format | marc |
| 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 Chichester, West Sussex Wiley [2017] 1 online resource txt rdacontent c rdamedia cr rdacarrier Wiley series in probability and statistics Includes bibliographical references and indexes Cover; Title Page; Copyright; Contents; Preface to the Second Edition; Preface to the First Edition; Part I Analysis of Non Fractional Time Series; Chapter 1 Models for Nonstationarity and Noninvertibility; 1.1 Statistics from the One-Dimensional Random Walk; 1.1.1 Eigenvalue Approach; 1.1.2 Stochastic Process Approach; 1.1.3 The Fredholm Approach; 1.1.4 An Overview of the Three Approaches; 1.2 A Test Statistic from a Noninvertible Moving Average Model; 1.3 The AR Unit Root Distribution; 1.4 Various Statistics from the Two-Dimensional Random Walk; 1.5 Statistics from the Cointegrated Process 1.6 Panel Unit Root TestsChapter 2 Brownian Motion and Functional Central Limit Theorems; 2.1 The Space L2 of Stochastic Processes; 2.2 The Brownian Motion; 2.3 Mean Square Integration; 2.3.1 The Mean Square Riemann Integral; 2.3.2 The Mean Square Riemann-Stieltjes Integral; 2.3.3 The Mean Square Ito Integral; 2.4 The Ito Calculus; 2.5 Weak Convergence of Stochastic Processes; 2.6 The Functional Central Limit Theorem; 2.7 FCLT for Linear Processes; 2.8 FCLT for Martingale Differences; 2.9 Weak Convergence to the Integrated Brownian Motion 2.10 Weak Convergence to the Ornstein-Uhlenbeck Process2.11 Weak Convergence of Vector-Valued Stochastic Processes; 2.11.1 Space Cq; 2.11.2 Basic FCLT for Vector Processes; 2.11.3 FCLT for Martingale Differences; 2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion; 2.12 Weak Convergence to the Ito Integral; Chapter 3 The Stochastic Process Approach; 3.1 Girsanov's Theorem: O-U Processes; 3.2 Girsanov's Theorem: Integrated Brownian Motion; 3.3 Girsanov's Theorem: Vector-Valued Brownian Motion; 3.4 The Cameron-Martin Formula; 3.5 Advantages and Disadvantages of the Present Approach Chapter 4 The Fredholm Approach4.1 Motivating Examples; 4.2 The Fredholm Theory: The Homogeneous Case; 4.3 The c.f. of the Quadratic Brownian Functional; 4.4 Various Fredholm Determinants; 4.5 The Fredholm Theory: The Nonhomogeneous Case; 4.5.1 Computation of the Resolvent-Case 1; 4.5.2 Computation of the Resolvent-Case 2; 4.6 Weak Convergence of Quadratic Forms; Chapter 5 Numerical Integration; 5.1 Introduction; 5.2 Numerical Integration: The Nonnegative Case; 5.3 Numerical Integration: The Oscillating Case; 5.4 Numerical Integration: The General Case; 5.5 Computation of Percent Points 5.6 The Saddlepoint ApproximationChapter 6 Estimation Problems in Nonstationary Autoregressive Models; 6.1 Nonstationary Autoregressive Models; 6.2 Convergence in Distribution of LSEs; 6.2.1 Model A; 6.2.2 Model B; 6.2.3 Model C; 6.2.4 Model D; 6.3 The c.f.s for the Limiting Distributions of LSEs; 6.3.1 The Fixed Initial Value Case; 6.3.2 The Stationary Case; 6.4 Tables and Figures of Limiting Distributions; 6.5 Approximations to the Distributions of the LSEs; 6.6 Nearly Nonstationary Seasonal AR Models; 6.7 Continuous Record Asymptotics; 6.8 Complex Roots on the Unit Circle Time-series analysis fast MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-119-13209-7 https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029708109&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 Time-series analysis fast MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Time-series analysis 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 | Time-series analysis fast MATHEMATICS / Applied bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Time-series analysis MATHEMATICS / Applied MATHEMATICS / Probability & Statistics / General Zeitreihenanalyse |
| url | https://onlinelibrary.wiley.com/doi/book/10.1002/9781119132165 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029708109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tanakakatsuto timeseriesanalysisnonstationaryandnoninvertibledistributiontheory |