Asymptotic Theory of Statistical Inference for Time Series

There has been much demand for the statistical analysis of dependent ob- servations in many fields, for example, economics, engineering and the nat- ural sciences. A model that describes the probability structure of a se- ries of dependent observations is called a stochastic process. 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 autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process- es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d- ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal- ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo- metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.