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.
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 im
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method
This book presents multivariate time series methods for the analysis and optimal control of feedback systems. Although ships’ autopilot systems are considered through the entire book, the methods set forth in this book can be applied to many other complicated, large, or noisy feedback control systems for which it is difficult to derive a model of the entire system based on theory in that subject area. The basic models used in this method are the multivariate autoregressive model with exogenous variables (ARX) model and the radial bases function net-type coefficients ARX model. The noise contribution analysis can then be performed through the estimated autoregressive (AR) model and various types of autopilot systems can be designed through the state–space representation of the models. The marine autopilot systems addressed in this book include optimal controllers for course-keeping motion, rolling reduction controllers with rudder motion, engine governor controllers, noise adaptive autopilots, route-tracking controllers by direct steering, and the reference course-setting approach. The methods presented here are exemplified with real data analysis and experiments on real ships. This book is highly recommended to readers who are interested in designing optimal or adaptive controllers not only of ships but also of any other complicated systems under noisy disturbance conditions.
Hirotugu Akaike is an internationally renowned researcher who profoundly affected how data and time-series are analyzed and modeled. His pioneering work is highly regarded and his talc method is frequently cited and applied in almost every area of the physical and social sciences. This book includes groundbreaking papers representing successive phases of Akaike's research which spanned more than 40 years.
This book presents a new statistical method of constructing a price index of a financial asset where the price distributions are skewed and heavy-tailed and investigates the effectiveness of the method. In order to fully reflect the movements of prices or returns on a financial asset, the index should reflect their distributions. However, they are often heavy-tailed and possibly skewed, and identifying them directly is not easy. This book first develops an index construction method depending on the price distributions, by using nonstationary time series analysis. Firstly, the long-term trend of the distributions of the optimal Box–Cox transformed prices is estimated by fitting a trend model with time-varying observation noises. By applying state space modeling, the estimation is performed and missing observations are automatically interpolated. Finally, the index is defined by taking the inverse Box–Cox transformation of the optimal long-term trend. This book applies the method to various financial data. For example, applying it to the sovereign credit default swap market where the number of observations varies over time due to the immaturity, the spillover effects of the financial crisis are detected by using the power contribution analysis measuring the information flows between indices. The investigations show that applying this method to the markets with insufficient information such as fast-growing or immature markets can be effective.
Statistical modeling is a critical tool in scientific research. This book provides comprehensive explanations of the concepts and philosophy of statistical modeling, together with a wide range of practical and numerical examples. The authors expect this work to be of great value not just to statisticians but also to researchers and practitioners in various fields of research such as information science, computer science, engineering, bioinformatics, economics, marketing and environmental science. It’s a crucial area of study, as statistical models are used to understand phenomena with uncertainty and to determine the structure of complex systems. They’re also used to control such systems, as well as to make reliable predictions in various natural and social science fields.
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
Hirotugu Akaike is an internationally renowned researcher who profoundly affected how data and time-series are analyzed and modeled. His pioneering work is highly regarded and his talc method is frequently cited and applied in almost every area of the physical and social sciences. This book includes groundbreaking papers representing successive phases of Akaike's research which spanned more than 40 years.
This book presents a new statistical method of constructing a price index of a financial asset where the price distributions are skewed and heavy-tailed and investigates the effectiveness of the method. In order to fully reflect the movements of prices or returns on a financial asset, the index should reflect their distributions. However, they are often heavy-tailed and possibly skewed, and identifying them directly is not easy. This book first develops an index construction method depending on the price distributions, by using nonstationary time series analysis. Firstly, the long-term trend of the distributions of the optimal Box–Cox transformed prices is estimated by fitting a trend model with time-varying observation noises. By applying state space modeling, the estimation is performed and missing observations are automatically interpolated. Finally, the index is defined by taking the inverse Box–Cox transformation of the optimal long-term trend. This book applies the method to various financial data. For example, applying it to the sovereign credit default swap market where the number of observations varies over time due to the immaturity, the spillover effects of the financial crisis are detected by using the power contribution analysis measuring the information flows between indices. The investigations show that applying this method to the markets with insufficient information such as fast-growing or immature markets can be effective.
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.
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