Asymptotic theory of statistical inference for time series
type: Item
instance of: scholarly article
title: Asymptotic theory of statistical inference for time series
zbMATH Open document ID: 0955.62088
author: Masanobu Taniguchi
author: Yoshihide Kakizawa
published in: Springer Series in Statistics
publication date: 2000-10-16T00:00:00Z
review text: The goal of the book is to provide modern statistical techniques and theory for stochastic processes. The presentation is based mainly on the recent results of the authors on asymptotic statistics, which appear for the first time in a monograph. The authors deal with a wide variety of stochastic processes, such as non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment processes, and continuous time processes. They develop estimation and testing theory, and also discriminant analysis, nonparametric methods, higher order asymptotic theory, large deviation principles, and saddlepoint approximations. The key concept of the book is local asymptotic normality (LAN), which gives a unified view for the time series asymptotic theory. Throughout the book, numerical examples to real data are given as applications. Chapter 1 reviews the elements of stochastic processes. Chapter 2 describes a general LAN theorem, which is applied to a wide class of vector valued processes. Chapter 3 discusses the asymptotic efficiency of estimators and tests for nonlinear models, non-ergodic models, and diffusion processes. In Chapter 4, Edgeworth expansions are used to derive higher order asymptotics (h.o.a.) of estimators and tests. This is done in view of statistical differential geometry. Basing on an infinite dimensional differential calculus of Wiener functionals, the h.o.a. are considered for diffusion processes. The h.o.a. are developed for transformations of statistics and iterative methods, e.g. the Newton-Raphson method. In Chapter 5 a modern asymptotic estimation and testing theory for long-memory processes is studied. These processes are very fashionable because of plausible applications in economics and financial modelling. The asymptotic theory for regression models with long-memory disturbances shows different features from that for short-memory processes. In Chapter 6 statistical analysis based on (nonlinear) integral functionals of spect…
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62Mxx
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 1517514
zbMATH Keywords: orthogonal increment processes
zbMATH Keywords: cluster analysis
zbMATH Keywords: LAN
zbMATH Keywords: non-Gaussian linear processes
zbMATH Keywords: discriminant analysis
zbMATH Keywords: local asymptotic normality
zbMATH Keywords: numerical examples
zbMATH Keywords: asymptotic efficiency
zbMATH Keywords: nonlinear models
zbMATH Keywords: non-ergodic models
zbMATH Keywords: diffusion processes
zbMATH Keywords: Edgeworth expansions
zbMATH Keywords: higher order asymptotics
zbMATH Keywords: Wiener functionals
zbMATH Keywords: long-memory processes
zbMATH Keywords: regression models
zbMATH Keywords: robustness
zbMATH Keywords: saddlepoint approximations
reviewed by: A. Kukush
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1517514