Time Series Analysis: Nonstationary and Noninvertible Distribution Theory, Second EditionISBN: 9781119132097
912 pages
April 2017

Description
Reflects the developments and new directions in the field since the publication of the first successful edition and contains a complete set of problems and solutions
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 a discussion on the distinction between deterministic and stochastic trends have been added. Three new chapters on longmemory discretetime and continuoustime 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 ten chapters, with a chapter on nonstationary panel added and located under Part I: Analysis of Nonfractional Time Series. Chapters 12 to 14 have been newly written under Part II: Analysis of Fractional Time Series. Chapter 12 discusses the basic theory of longmemory processes by introducing ARFIMA models and the fractional Brownian motion (fBm). Chapter 13 is concerned with the computation of distributions of quadratic functionals of the fBm and its ratio. Next, Chapter 14 introduces the fractional Ornstein–Uhlenbeck process, on which the statistical inference is discussed. Finally, Chapter 15 gives a complete set of solutions to problems posed at the end of most sections. This new edition features:
• Sections to discuss nonstationary panel data analysis, the problem of differentiating between deterministic and stochastic trends, and nonstationary processes of local deviations from a unit root
• Consideration of the maximum likelihood estimator of the drift parameter, as well as asymptotics as the sampling span increases
• Discussions on not only nonstationary but also noninvertible time series from a theoretical viewpoint
• New topics such as the computation of limiting local powers of panel unit root tests, the derivation of the fractional unit root distribution, and unit root tests under the fBm error
Time Series Analysis: Nonstationary and Noninvertible Distribution Theory, Second Edition, is a reference for graduate students in econometrics or time series analysis.
Katsuto Tanaka, PhD, is a professor in the Faculty of Economics at Gakushuin University and was previously a professor at Hitotsubashi University. He is a recipient of the Tjalling C. Koopmans Econometric Theory Prize (1996), the Japan Statistical Society Prize (1998), and the Econometric Theory Award (1999). Aside from the first edition of Time Series Analysis (Wiley, 1996), Dr. Tanaka had published five econometrics and statistics books in Japanese.
Table of Contents
Preface to first Edition
Preface to Second Edition
Part I: Analysis of NonFractional Time Series
Chapter 1: Models for Nonstationarity and Noninvertibility
1.1 Statistics from the OneDimensional Random Walk
1.2 A Test Statistic from a Noninvertible Moving Average Model
1.3 The AR Unit Root Distribution
1.4 Various Statistics from the TwoDimensional Random Walk
1.5 Statistics from the Cointegrated Process
1.6 Panel Unit Root Tests
Chapter 2: Brownian Motions and Functional Central Limit Theorems
2.1 The Space L2 of Stochastic Processes
2.2 The Brownian Motion
2.3 Mean Square Integration
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 OrnsteinUhlenbeck Process
2.11 Weak Convergence of VectorValued Stochastic Processes
2.12 Weak Convergence to the Ito Integral
Chapter 3: The Stochastic Process Approach
3.1 Girsanov's Theorem: OU Processes
3.2 Girsanov's Theorem: Integrated Brownian Motion
3.3 Girsanov's Theorem: VectorValued 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
4.6 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
6.3 The c.f.s for the Limiting Distributions of LSEs
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
7.5 The Pseudolocal MLE
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
8.3 Equivalence of the LM Test with the LBI or LBIU Test
8.4 Various Unit Root Tests
8.5 Integral Expressions for the Limiting Powers
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
Chapter 9: Unit Root Tests in Moving Average Models
9.1 Introduction
9.2 The LBI and LBIU Tests
9.3 The Relationship with the Test Statistics in Differenced Form
9.4 Performance of the LBI and LBIU Tests
9.5 Seasonal Unit Root Tests
9.6 Unit Root Tests in the Dependent Case
9.7 The Relationship with Testing in the State Space Model
Chapter 10: Asymptotic Properties of Nonstationary Panel Unit Root Tests
10.1 Introduction
10.2 Panel Autoregressive Models
10.3 Panel Moving Average Models
10.4 Panel Stationarity Tests
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
11.7 Determination of the Cointegration Rank
11.8 Higher Order Cointegration
Part II: Analysis of Fractional Time Series
Chapter 12: ARFIMA Models and the Fractional Brownian Motion
12.1 Nonstationary Fractional Time Series
12.2 Testing for the Fractional Integration Order
12.3 Estimation for the Fractional Integration Order
12.4 Stationary LongMemory Processes
12.5 The Fractional Brownian Motion
12.6 FCLT for LongMemory Processes
12.7 Fractional Cointegration
12.8 The Wavelet Method for ARFIMA Models and the fBm
Chapter 13: Statistical Inference Associated with the Fractional Brownian Motion
13.1 Introduction
13.2 A Simple ContinuousTime Model Driven by the fBm
13.3 Quadratic Functionals of the Brownian Motion
13.4 Derivation of the c.f.
13.5 Martingale Approximation to the fBm
13.6 The Fractional Unit Root Distribution
13.7 The Unit Root Test under the fBm Error
Chapter 14: Maximum Likelihood Estimation for the Fractional OrnsteinUhlenbeck Process
14.1 Introduction
14.2 Estimation of the Drift: Ergodic Case
14.3 Estimation of the Drift: NonErgodic Case
14.4 Estimation of the Drift: Boundary Case
14.5 Computation of Distributions and Moments of the MLE and MCE
14.6 The MLEBased Unit Root Test under the fBm Error
14.7 Concluding Remarks
Chapter 15: Solutions to Problems
References
Author Index
Subject Index
Author Information
Katsuto Tanaka, PhD, is a professor in the Faculty of Economics at Gakushuin University and was previously a professor at Hitotsubashi University. He is a recipient of the Tjalling C. Koopmans Econometric Theory Prize (1996), the Japan Statistical Society Prize (1998), and the Econometric Theory Award (1999). Aside from the first edition of Time Series Analysis (Wiley, 1996), Dr. Tanaka had published five econometrics and statistics books in Japanese.