Time Series Analysis : Nonstationary and Noninvertible Distribution Theory.

Other records:
Tanaka, Katsuto.
2nd ed.
New York : John Wiley & Sons, Incorporated, 2017.
Wiley Series in Probability and Statistics Ser.
Wiley Series in Probability and Statistics Ser. ; v.4
1 online resource (906 pages)
Time-series analysis.
Electronic books.
Title Page
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 >
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 Testing for d in ARFIMA Models Testing for the Existence of Noise Testing for Fractional Cointegration 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 Case of H = 1/2 Case of H >
13.4.2 Fredholm Approach via the Fredholm Determinant Case of H = 1/2 Case of H >
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
Author Index
Subject Index
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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Print version: Tanaka, Katsuto Time Series Analysis
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