The main theme of the present edition remains the same and reflects the developments and new directions in the field since the publication of the first edition. In particular, the discussion on nonstationary panel data analysis has been added and new chapters on long-memory discrete-time and continuous-time processes have been created, whereas some chapters have been merged and some sections deleted.
This edition is divided into two parts; {\it Part I: Analysis of Non-Fractional Time Series} and {\it Part II: Analysis of Fractional Time Series}, where Part I consisits of Chapters 1 through 11, while Part II consists of Chapters 12 through 14. The distinction between non-fractional and fractional time series is concerned with the integration order of nonstationary time series. Part I assumes the integration order to be a positive integer, whereas Part II relaxes that assumption to allow the integration order to be any positive real number.
Chapter 1 is essentially the same as the first edition, except for the addition of an introductory description on nonstationary panels, and is a prelude to subsequent chapters. The three approaches, which I call the {\it eigenvalue, stochastic process, and Fredholm approaches}, to the analysis of non-fractional time series are introduced through simple examples. Chapter 2 merged Chapters 2 and 3 of the first edition and discusses the Brownian motion, the Ito integral, the functional central limit theorem and so on.
Chapters 3 and 4 discuss fully the {\it stochastic process approach} and the {\it Fredholm approach}, respectively. These approaches are used to derive limiting characteristic functions of nonstandard statistics that are quadratic functionals of the Brownian motion or its ratio. Chapter 5 is concerned with numerical integration for computing distribution functions via inversion of characteristic functions derived from the stochastic process approach or the Fredholm approach.
Chapters 6 through 11 deal with unit root and cointegration problems. Chapters except Chapter 10 were main chapters of the first edition. New topics such as unit root tests under structural breaks, differentiating between stochastic and deterministic trends, and so on have been added. Chapter 10 has been added to discuss nonstationary panel data models, where our main concern is to compute limiting local powers of various panel unit root tests. For that purpose the moving average models are also considered in addition to autoregressive models.
Chapters 12 through 14 have been written newly under {\it 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). The wavelet method is also introduced to deal with ARFIMA models and the fBm. Chapter 13 is concerned with the computation of distributions of quadratic functionals of the fBm and its ratio, where the computation of the fractional unit root distribution remains to be done, whereas an approximation to the true distribution is proposed and computed. Chapter 14 introduces the fractional Ornstein-Uhlenbeck process, on which the statistical inference is discussed. In particular, the maximum likelihood estimator of the drift parameter is considered, and asymptotics as the sampling span increases are discussed.
Chapter 15, the last chapter, gives a complete set of solutions to problems posed at the end of most sections.
There are about 140 figures and 60 tables. Most of these are of limiting distributions of nonstandard statistics. They are all produced by the methods described in this edition and include many distributions which have never appeared in the literature.
The present edition is dedicated to my wife, Yoshiko, who died in 1999.
Katsuto Tanaka