||Number of Pages
||INTRODUCTION TO TIME SERIES MODELING
Author: Genshiro Kitagawa
Description: In time series modeling, the behavior of a certain phenomenon is expressed 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 learn fundamental methods of time series modeling. Illustrating how to build models for time series using basic methods, Introduction to Time Series Modeling covers numerous time series models and the various tools for handling them. This book employs the state-space model as a generic tool for time series modeling and presents convenient recursive filtering and smoothing methods, including the Kalman filter, the non-Gaussian filter, and the sequential Monte Carlo filter, for the state-space models. Taking a unified approach to model evaluation based on the entropy maximization principle advocated by Dr. Akaike, the author derives various methods of parameter estimation, such as the least squares method, the maximum likelihood method, recursive estimation for state-space models, and model selection by the Akaike information criterion (AIC). Along with simulation methods, he also covers standard stationary time series models, such as AR and ARMAmodels, as well as nonstationary time series models, including the locally stationary AR model, the trend model, the seasonal adjustment model, and the time-varying coefficient AR model. With a focus on the description, modeling, prediction, and signal extraction of times series, this book provides basic tools for analyzing time series that arise in real-world problems. It encourages readers to build models for their own real-life problems.
Table of Content: 1.Introduction and preparatory Analysis 2. The Covariance Function 3. The Power Spectrum and the Periodogram 4. Statistical Modeling 5. The Least Squares Method 6. Analysis of Time Series Using ARMAModels 7. Estimation of an AR Model 8. The Locally Stationery AR Model 9. Analysis of Time Series wiht a State-Space Model 10. Estimation of the ARMA Model 11. Estimation of Trends 12. The Seasonal Adjustment Model 13. Time -Varying Coefficient AR Model 14. Non-Gaussian State-Space Model 15. The Sequential Monte Carlo Filter 16. Simulation - Algorithms for Nonlinear Qptimization - Derivation of Levinson’s Algorithm - Derivation of the Kalman Filter - Algorithm for the Monte Carlo Filter - Bibliography