Praise for the first edition:
[This book] reflects the extensive experience and significant contributions of the author to non-linear and non-Gaussian modeling. ... [It] is a valuable book, especially with its broad and accessible introduction of models in the state-space framework.
-Statistics in Medicine
What distinguishes this book from comparable introductory texts is the use of state-space modeling. Along with this come a number of valuable tools for recursive filtering and smoothing, including the Kalman filter, as well as non-Gaussian and sequential Monte Carlo filters.
-MAA Reviews
Introduction to Time Series Modeling with Applications in R, Second Edition 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.
About the Author:
Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.
Autorentext
Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.
Klappentext
Praise for the first edition:
[This book] reflects the extensive experience and significant contributions of the author to non-linear and non-Gaussian modeling. ... [It] is a valuable book, especially with its broad and accessible introduction of models in the state-space framework.
-Statistics in Medicine
What distinguishes this book from comparable introductory texts is the use of state-space modeling. Along with this come a number of valuable tools for recursive filtering and smoothing, including the Kalman filter, as well as non-Gaussian and sequential Monte Carlo filters.
-MAA Reviews
Introduction to Time Series Modeling with Applications in R, Second Edition 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.
About the Author:
Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.
Inhalt
1 Introduction and Preparatory Analysis
1.1 Time Series Data
1.2 Classi cation of Time Series
1.3 Objectives of Time Series Analysis
1.4 Pre-processing of Time Series
1.4.1 Transformation of variables
1.4.2 Differencing
1.4.3 Month-to-month basis and year-over-year
1.4.4 Moving average
1.5 Organization of This Book
2 The Covariance Function
2.1 The Distribution of Time Series and Stationarity
2.2 The Autocovariance Function of Stationary Time Series
2.3 Estimation of the Autocovariance Function
2.4 Multivariate Time Series and Scatterplots
2.5 Cross-covariance Function and Cross-correlation Function
3 The Power Spectrum and the Periodogram
3.1 The Power Spectrum
3.2 The Periodogram
3.3 Averaging and Smoothing of the Periodogram
3.4 Computational Method of Periodogram
3.5 Computation of the Periodogram by Fast Fourier Transform
4 Statistical Modeling
4.1 Probability Distributions and Statistical Models
4.2 K-L Information and Entropy Maximization Principle
4.3 Estimation of the K-L Information and the Log-likelihood
4.4 Estimation of Parameters by the Maximum Likelihood Method
4.5 AIC (Akaike Information Criterion)
4.5.1 Evaluation of C1
4.5.2 Evaluation of C3
4.5.3 Evaluation of C2
4.5.4 Evaluation of C and AIC
4.6 Transformation of Data
5 The Least Squares Method
5.1 Regression Models and the Least Squares Method
5.2 Householder Transformation Method
5.3 Selection of Order by AIC
5.4 Addition of Data and Successive Householder Reduction
5.5 Variable Selection by AIC
6 Analysis of Time Series Using ARMA Models
6.1 ARMA Model
6.2 The Impulse Response Function
6.3 The Autocovariance Function
6.4 The Relation Between AR Coef cients and PARCOR 98
6.5 The Power Spectrum of the ARMA Process 98
6.6 The Characteristic Equation 102
6.7 The Multivariate AR Model 106
7 Estimation of an AR Model
7.1 Fitting an AR Mode
7.2 Yule-Walker Method and Levinson's Algorithm
7.3 Estimation of an AR Model by the Least Squares Method
7.4 Estimation of an AR Model by the PARCOR Method
7.5 Large Sample Distribution of the Estimates
7.6 Estimation of Multivariate AR Model by Yule-Walker Method
7.7 Estimation of Multivariate AR Model by Least Squares Method
8 The Locally Stationary AR Model
8.1 Locally Stationary AR Model
8.2 Automatic Partitioning of the Time Interval
8.3 Precise Estimation of the Change Point
…