Masanobu Taniguchi, Yoshihide Kakizawa, "Asymptotic Theory of Statistical Inference for Time Series "
Springer | 2000 | ISBN: 0387950397 | 661 pages

The primary aims of this book are to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA and ARMA processes. A wide variety of stochastic processes, e.g., non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss the usual estimation and testing theory and also many other statistical methods and techniques, e.g., discriminant analysis, nonparametric methods, semiparametric approaches, higher order asymptotic theory in view of differential geometry, large deviation principle and saddlepoint approximation. Because it is difficult to use the exact distribution theory, the discussion is based on the asymptotic theory. The optimality of various procedures is often shown by use of the local asymptotic normality (LAN) which is due to Le Cam. The LAN gives a unified view for ! the time series asymptotic theory. 

Very good book for students major in time series or stochastic processes. Strong commend!!

Ch1. Elements of stochastic processes

Ch2. LAN for  stochastic processes

Ch3. Asymptotic theory of estimation and tesing

Ch4. High order  Asymptotic theory of stochastic processes

Ch5. Asymptotic theory for long memory process

Ch6. Statistical analysis based on spectral analysis

Ch7. Discriminat analysis for stationary time series

Ch8. LAD and SA for stochastic processes

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