Chapman & Hall/CRC, 2010. 305 pages.
This book aims at introducing and explaining basic methods of building models for time series. In time series modeling, we try to express the behavior of a certain phenomenon in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important and useful to lea basic methods of time series modeling. In this book, many time series models and various tools for handling them are introduced.
The main feature of this book is to use the state space model as a generic tool for time series modeling. Three types of recursive filtering and smoothing methods, the Kalman filter, the non-Gaussian filter, and the sequential Monte Carlo filter, are presented as convenient tools for the state space models. Further, in this book, a unified approach to model evaluation is introduced based on the entropymaximization principle advocated by Dr. Akaike. Based on this unified approach, various methods of parameter estimation, such as the least squares method, the maximum likelihood method, the recursive estimation for the state space models, and the model selection by the information criterion AIC, are derived.
After introducing standard stationary time series models, such as AR model and ARMA model, we present various nonstationary time series models, such as the locally stationary AR model, the trend model, the seasonal adjustment model, and the time-varying coefficient AR model
and nonlinear non-Gaussian models. The simulation methods are also shown. The principal aim of the author will be achieved when readers succeed in building models for their own real-world problems.
This book aims at introducing and explaining basic methods of building models for time series. In time series modeling, we try to express the behavior of a certain phenomenon in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important and useful to lea basic methods of time series modeling. In this book, many time series models and various tools for handling them are introduced.
The main feature of this book is to use the state space model as a generic tool for time series modeling. Three types of recursive filtering and smoothing methods, the Kalman filter, the non-Gaussian filter, and the sequential Monte Carlo filter, are presented as convenient tools for the state space models. Further, in this book, a unified approach to model evaluation is introduced based on the entropymaximization principle advocated by Dr. Akaike. Based on this unified approach, various methods of parameter estimation, such as the least squares method, the maximum likelihood method, the recursive estimation for the state space models, and the model selection by the information criterion AIC, are derived.
After introducing standard stationary time series models, such as AR model and ARMA model, we present various nonstationary time series models, such as the locally stationary AR model, the trend model, the seasonal adjustment model, and the time-varying coefficient AR model
and nonlinear non-Gaussian models. The simulation methods are also shown. The principal aim of the author will be achieved when readers succeed in building models for their own real-world problems.