http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
nonstationary and noninvertible distribution theory
"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 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 ten chapters, with a chapter on nonstationary panel added and located under Part I: Analysis of Non-fractional 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 long-memory 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."--Publisher description.
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.
Katsuto Tanaka, professor of statistics and econometrics, Gakushuin University, Tokyo.
Includes bibliographical references and indexes.
Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force. WlAbNL
Wiley Series in Probability and Statistics
Hoboken, NJ : John Wiley & Sons, Inc., [2017]