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Introduction to Time Series Modeling with Applications in R

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Titre :	Introduction to Time Series Modeling with Applications in R
Type de document :	Monographie imprimée
Editeur :	Chapman & Hall, 2022
ISBN/ISSN/EAN :	978-0-367-49424-7
Format :	1 vol. (340 p.)
Langues:	Anglais
Index. décimale :	519. 55
Résumé :	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.
Sommaire :	1 Introduction and Preparatory Analysis 1.1 Time Series Data 1.2 Classiﬁcation 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 Coefﬁcients 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 8.4 Posterior Probability of the Change Point 9 Analysis of Time Series with a State-Space Model 9.1 The State-Space Model 9.2 State Estimation via the Kalman Filter 9.3 Smoothing Algorithms 9.4 Long-term Prediction of the State 9.5 Prediction of Time Series 9.6 Likelihood Computation and Parameter Estimation for Time Series Models 9.7 Interpolation of Missing Observations 10 Estimation of the ARMA Model 10.1 State-Space Representation of the ARMA Model 10.2 Initial State Distribution for an AR Model 10.3 Initial State Distribution of an ARMA Model 10.4 Maximum Likelihood Estimates of an ARMA Model 10.5 Initial Estimates of Parameters 11 Estimation of Trends 11.1 The Polynomial Trend Model 11.2 Trend Component Model – Model for Gradual Changes 11.3 Trend Model 12 The Seasonal Adjustment Model 12.1 Seasonal Component Model 12.2 Standard Seasonal Adjustment Model 12.3 Decomposition Including an AR Component 12.4 Decomposition Including a Trading-day Effect 13 Time-Varying Coefﬁcient AR Model 13.1 Time-varying Variance Model 13.2 Time-varying Coefﬁcient AR Model 13.3 Estimation of the Time-varying Spectrum 13.4 The Assumption on System Noise for the Time-varying Coefﬁcient AR Model 13.5 Abrupt Changes of Coefﬁcients 14 Non-Gaussian State-Space Model 14.1 Necessity of Non-Gaussian Models 14.2 Non-Gaussian State-Space Models and State Estimation 14.3 Numerical Computation of the State Estimation Formula 14.4 Non-Gaussian Trend Model 14.5 A Time-varying Variance Model 14.6 Further Applications of Non-Gaussian State-Space Model 14.6.1 Processing of the outliers by a mixture of Gaussian distributions 14.6.2 A nonstationary discrete process 14.6.3 A direct method of estimating the time-varying variance 14.6.4 Nonlinear state-spece models 15 Particle Filter 15.1 The Nonlinear Non-Gaussian State-Space Model and Approximations of Distributions 15.2 Particle Filter 15.2.1 One-step-ahead prediction 15.2.2 Filtering 15.2.3 Algorithm for the particle ﬁlter 15.2.4 Likelihood of a model 15.2.5 On the re-sampling method 15.2.6 Numerical examples 15.3 Particle Smoothing Method 15.4 Nonlinear Smoothing 16 Simulation 16.1 Generation of Uniform Random Numbers 16.2 Generation of White Noise 16.2.1 χ2 distribution 16.2.2 Cauchy distribution 16.2.3 Arbitrary distribution 16.3 Simulation of ARMA models 16.4 Simulation Using a State-Space Model 16.5 Simulation with Non-Gaussian Model A Algorithms forNonlinearOptimization B Derivation ofLevinson’sAlgorithm C Derivation of the Kalman Filter and Smoother Algorithms C.1 Kalman Filter C.2 Smoothing D Algorithm for the Particle Filter D.1 One-step-ahead Prediction D.2 Filter D.3 Smoothing 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