Introduction to time series modeling with aplications in R/ Genshiro Kitagawa

Includes Bibliography and index

Introduction and preparatory analysis -- The Covariance function -- The Power spectrum and the periodogram -- Statistical modeling -- The Least square method -- Analysis of time series using ARMA models -- Estimation of an AR model -- The Locally stationary AR model -- Analysis of time series with a state-space model -- Estimation of the ARMA model -- Estimation of trends -- The Seasonal adjustment model -- Time varying coefficient AR model -- Non-Gaussian state-space model -- Particle filter -- Simulation -- A Algorithms for nonlinear optimization -- B Derivation of Levinson's algorithm -- C Derivation of the kalman filter and smoother algorithms -- D Algorithm for the particle filter

This book covers numerous stationary and nonstationary time series models and tools for estimating and utilizing them. The goal of this book is to enable readers to build their own models to understand, predict and master time series. The second edition makes it possible for readers to reproduce examples in this book by using the freely available R package TSSS to perform computations for their own real-world time series problems.

This book employs the state-space model as a generic tool for time series modeling and presents the Kalman filter, the non-Gaussian filter and the particle filter as convenient tools for recursive estimation for state-space models. Further, it also takes a unified approach based on the entropy maximization principle and employs various methods of parameter estimation and model selection, including the least squares method, the maximum likelihood method, recursive estimation for state-space models and model selection by AIC.

Along with the standard stationary time series models, such as the AR and ARMA models, the book also introduces nonstationary time series models such as the locally stationary AR model, the trend model, the seasonal adjustment model, the time-varying coefficient AR model and nonlinear non-Gaussian state-space models.