Time series analysis nonstationary and noninvertible distribution theory - Tanaka, Katsuto 1950- (Wiley, 2017)
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