Time series analysis : nonstationary and noninvertible distribution theory / Katsuto Tanaka.

Format:

Book

Author/Creator:

Tanaka, Katsuto, 1950- author.

Series:

Wiley series in probability and statistics.

THEi Wiley ebooks.

Wiley Series in Probability and Statistics

THEi Wiley ebooks

Language:

English

Subjects (All):

Time-series analysis.

Physical Description:

1 online resource (906 pages).

Edition:

Second edition.

Place of Publication:

Hoboken, New Jersey : Wiley, 2017.

System Details:

Access using campus network via VPN at home (THEi Users Only).

Summary:

This revised and expanded edition reflects the developments and new directions in the field since the publication of the first edition. In particular, sections on nonstationary panel data analysis and the discussion on the distinction between deterministic and stochastic trends have been added. Three new chapters on long-memory discrete-time and continuous-time processes have also been created, whereas some chapters have been merged and some sections deleted. The first eleven chapters of the first edition have been compressed into eight chapters and located under Part I: Analysis of Non-Fractional Time Series. Chapters nine through eleven have been newly written under Part II: Analysis of Fractional Time Series. The last chapter gives a complete set of solutions to problems posed at the end of most sections of each chapter. Most of the problems are concerned with corroborating the results described in the text, so that one can gain a better understanding of details of the discussions. Figures are produced by the methods described in this edition and include many distributions whose computational results have never appeared in the literature. The book can be used as a text for graduate students in econometrics or time series analysis. A general knowledge of mathematical statistics, including the theory of stationary processes, is presupposed, although the necessary material is offered in the text and problems of this book. Some knowledge of a programming language and computerized algebra is also useful.

Contents:

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 Tests

Chapter 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 Process

2.11 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 Approach.

4.1 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 Approximation

Chapter 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

6.9 Autoregressive Models with Multiple Unit Roots

Chapter 7 Estimation Problems in Noninvertible Moving Average Models

7.1 Noninvertible Moving Average Models

7.2 The Local MLE in the Stationary Case

7.3 The Local MLE in the Conditional Case

7.4 Noninvertible Seasonal Models

7.4.1 The Stationary Case

7.4.2 The Conditional Case

7.4.3 Continuous Record Asymptotics

7.5 The Pseudolocal MLE

7.5.1 The Stationary Case

7.5.2 The Conditional Case

7.6 Probability of the Local MLE at Unity

7.7 The Relationship with the State Space Model

Chapter 8 Unit Root Tests in Autoregressive Models

8.1 Introduction

8.2 Optimal Tests.

8.2.1 The LBI Test

8.2.2 The LBIU Test

8.3 Equivalence of the LM Test with the LBI or LBIU Test

8.3.1 Equivalence with the LBI Test

8.3.2 Equivalence with the LBIU Test

8.4 Various Unit Root Tests

8.5 Integral Expressions for the Limiting Powers

8.5.1 Model A

8.5.2 Model B

8.5.3 Model C

8.5.4 Model D

8.6 Limiting Power Envelopes and Point Optimal Tests

8.7 Computation of the Limiting Powers

8.8 Seasonal Unit Root Tests

8.9 Unit Root Tests in the Dependent Case

8.10 The Unit Root Testing Problem Revisited

8.11 Unit Root Tests with Structural Breaks

8.12 Stochastic Trends Versus Deterministic Trends

8.12.1 Case of Integrated Processes

8.12.2 Case of Near-Integrated Processes

8.12.3 Some Simulations

Chapter 9 Unit Root Tests in Moving Average Models

9.1 Introduction

9.2 The LBI and LBIU Tests

9.2.1 The Conditional Case

9.2.2 The Stationary Case

9.3 The Relationship with the Test Statistics in Differenced Form

9.4 Performance of the LBI and LBIU Tests

9.4.1 The Conditional Case

9.4.2 The Stationary Case

9.5 Seasonal Unit Root Tests

9.5.1 The Conditional Case

9.5.2 The Stationary Case

9.5.3 Power Properties

9.6 Unit Root Tests in the Dependent Case

9.6.1 The Conditional Case

9.6.2 The Stationary Case

9.7 The Relationship with Testing in the State Space Model

9.7.1 Case (I)

9.7.2 Case (II)

9.7.3 Case (III)

9.7.4 The Case of the Initial Value Known

Chapter 10 Asymptotic Properties of Nonstationary Panel Unit Root Tests

10.1 Introduction

10.2 Panel Autoregressive Models

10.2.1 Tests Based on the OLSE

10.2.2 Tests Based on the GLSE

10.2.3 Some Other Tests

10.2.4 Limiting Power Envelopes

10.2.5 Graphical Comparison

10.3 Panel Moving Average Models

10.3.1 Conditional Case

10.3.2 Stationary Case.

10.3.3 Power Envelope

10.3.4 Graphical Comparison

10.4 Panel Stationarity Tests

10.4.1 Limiting Local Powers

10.4.2 Power Envelope

10.4.3 Graphical Comparison

10.5 Concluding Remarks

Chapter 11 Statistical Analysis of Cointegration

11.1 Introduction

11.2 Case of No Cointegration

11.3 Cointegration Distributions: The Independent Case

11.4 Cointegration Distributions: The Dependent Case

11.5 The Sampling Behavior of Cointegration Distributions

11.6 Testing for Cointegration

11.6.1 Tests for the Null of No Cointegration

11.6.2 Tests for the Null of Cointegration

11.7 Determination of the Cointegration Rank

11.8 Higher Order Cointegration

11.8.1 Cointegration in the I(d) Case

11.8.2 Seasonal Cointegration

Part II Analysis of Fractional Time Series

Chapter 12 ARFIMA Models and the Fractional Brownian Motion

12.1 Nonstationary Fractional Time Series

12.1.1 Case of Case of d = 1/2

12.1.2 Case of Case of d &gt

1/2

12.2 Testing for the Fractional Integration Order

12.2.1 i.i.d. Case

12.2.2 Dependent Case

12.3 Estimation for the Fractional Integration Order

12.3.1 i.i.d. Case

12.3.2 Dependent Case

12.4 Stationary Long-Memory Processes

12.5 The Fractional Brownian Motion

12.6 FCLT for Long-Memory Processes

12.7 Fractional Cointegration

12.7.1 Spurious Regression in the Fractional Case

12.7.2 Cointegrating Regression in the Fractional Case

12.7.3 Testing for Fractional Cointegration

12.8 The Wavelet Method for ARFIMA Models and the fBm

12.8.1 Basic Theory of the Wavelet Transform

12.8.2 Some Advantages of the Wavelet Transform

12.8.3 Some Applications of the Wavelet Analysis

12.8.3.1 Testing for d in ARFIMA Models

12.8.3.2 Testing for the Existence of Noise

12.8.3.3 Testing for Fractional Cointegration

12.8.3.4 Unit Root Tests.

Chapter 13 Statistical Inference Associated with the Fractional Brownian Motion

13.1 Introduction

13.2 A Simple Continuous-Time Model Driven by the fBm

13.3 Quadratic Functionals of the Brownian Motion

13.4 Derivation of the c.f.

13.4.1 Stochastic Process Approach via Girsanov's Theorem

13.4.1.1 Case of H = 1/2

13.4.1.2 Case of H &gt

13.4.2 Fredholm Approach via the Fredholm Determinant

13.4.2.1 Case of H = 1/2

13.4.2.2 Case of H &gt

13.5 Martingale Approximation to the fBm

13.6 The Fractional Unit Root Distribution

13.6.1 The FD Associated with the Approximate Distribution

13.6.2 An Interesting Moment Property

13.7 The Unit Root Test Under the fBm Error

Chapter 14 Maximum Likelihood Estimation for the Fractional Ornstein-Uhlenbeck Process

14.1 Introduction

14.2 Estimation of the Drift: Ergodic Case

14.2.1 Asymptotic Properties of the OLSEs

14.2.2 The MLE and MCE

14.3 Estimation of the Drift: Non-ergodic Case

14.3.1 Asymptotic Properties of the OLSE

14.3.2 The MLE

14.4 Estimation of the Drift: Boundary Case

14.4.1 Asymptotic Properties of the OLSEs

14.4.2 The MLE and MCE

14.5 Computation of Distributions and Moments of the MLE and MCE

14.6 The MLE-based Unit Root Test Under the fBm Error

14.7 Concluding Remarks

Chapter 15 Solutions to Problems

References

Author Index

Subject Index

EULA.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-119-13211-8

1-119-13213-4

1-119-13216-9

OCLC:

962750334