The primary aim of this book is 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, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

1 Elements of Stochastic Processes.- 1.1 Introduction.- 1.2 Stochastic Processes.- 1.3 Limit Theorems.- Problems.- 2 Local Asymptotic Normality for Stochastic Processes.- 2.1 General Results for Local Asymptotic Normality.- 2.2 Local Asymptotic Normality for Linear Processes.- Problems.- 3 Asymptotic Theory of Estimation and Testing for Stochastic Processes.- 3.1 Asymptotic Theory of Estimation and Testing for Linear Processes.- 3.2 Asymptotic Theory for Nonlinear Stochastic Models.- 3.3 Asymptotic Theory for Continuous Time Processes.- Problems.- 4 Higher Order Asymptotic Theory for Stochastic Processes.- 4.1 Introduction to Higher Order Asymptotic Theory.- 4.2 Valid Asymptotic Expansions.- 4.3 Higher Order Asymptotic Estimation Theory for Discrete Time Processes in View of Statistical Differential Geometry.- 4.4 Higher Order Asymptotic Theory for Continuous Time Processes.- 4.5 Higher Order Asymptotic Theory for Testing Problems.- 4.6 Higher Order Asymptotic Theory for Normalizing Transformations.- 4.7 Generalization of LeCam's Third Lemma and Higher Order Asymptotics of Iterative Methods.- Problems.- 5 Asymptotic Theory for Long-Memory Processes.- 5.1 Some Elements of Long-Memory Processes.- 5.2 Limit Theorems for Fundamental Statistics.- 5.3 Estimation and Testing Theory for Long-Memory Processes.- 5.4 Regression Models with Long-Memory Disturbances.- 5.5 Semiparametric Analysis and the LAN Approach.- Problems.- 6 Statistical Analysis Based on Functionals of Spectra.- 6.1 Estimation of Nonlinear Functionals of Spectra.- 6.2 Application to Parameter Estimation for Stationary Processes.- 6.3 Asymptotically Efficient Nonparametric Estimation of Functionals of Spectra in Gaussian Stationary Processes.- 6.4 Robustness in the Frequency Domain Approach.- 6.5 NumericalExamples.- Problems.- 7 Discriminant Analysis for Stationary Time Series.- 7.1 Basic Formulation.- 7.2 Standard Methods for Gaussian Stationary Processes.- 7.3 Discriminant Analysis for Non-Gaussian Linear Processes.- 7.4 Nonparametric Approach for Discriminant Analysis.- 7.5 Parametric Approach for Discriminant Analysis.- 7.6 Derivation of Spectral Expressions to Divergence Measures Between Gaussian Stationary Processes.- 7.7 Miscellany.- Problems.- 8 Large Deviation Theory and Saddlepoint Approximation for Stochastic Processes.- 8.1 Large Deviation Theorem 538 8.2 Asymptotic Efficiency for Gaussian Stationary Processes:Large Deviation Approach.- 8.3 Large Deviation Results for an Ornstein-Uhlenbeck Process.- 8.4 Saddlepoint Approximations for Stochastic Processes.- Problems.- A.1 Mathematics.- A.2 Probability.- A.3 Statistics.