Reviews
"There is scarcely a standard technique that the reader will find left out ... this book is highly recommended for those requiring a ready introduction to applicable methods in time series and serves as a useful resource for pedagogical purposes." --International Statistical Review(2014), 82 "Current time series theory for practice is well summarized in this book." --Emmanuel Parzen, Texas A&M University "What an extraordinary range of topics covered, all very insightfully. I like [the authors'] innovations very much, such as the AR factor table." --David Findley, U.S. Census Bureau (retired) "... impressive coverage of the scope of time series analysis in both frequency and time domain ... One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. ... I commend the authors for having included a number of topics on nonstationary processes ... an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. ... the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book ..." --Hernando Ombao, Journal of the American Statistical Association, March 2013 "The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book's material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis." --Hassan S. Bakouch, Journal of Applied Statistics, 2012, "Current time series theory for practice is well summarized in this book." --Emmanuel Parzen, Texas A&M University "What an extraordinary range of topics covered, all very insightfully. I like [the authors'] innovations very much, such as the AR factor table." --David Findley, U.S. Census Bureau (retired) "... impressive coverage of the scope of time series analysis in both frequency and time domain ... One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. ... I commend the authors for having included a number of topics on nonstationary processes ... an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. ... the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book ..." --Hernando Ombao, Journal of the American Statistical Association, March 2013 "The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book's material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis." --Hassan S. Bakouch, Journal of Applied Statistics, 2012, "Current time series theory for practice is well summarized in this book." 'e"Emmanuel Parzen, Texas A&M University "What an extraordinary range of topics covered, all very insightfully. I like [the authors'e(tm)] innovations very much, such as the AR factor table." 'e"David Findley, U.S. Census Bureau (retired) "'e¦ impressive coverage of the scope of time series analysis in both frequency and time domain 'e¦ One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. 'e¦ I commend the authors for having included a number of topics on nonstationary processes 'e¦ an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. 'e¦ the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book 'e¦" 'e"Hernando Ombao, Journal of the American Statistical Association, March 2013 "The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book'e(tm)s material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis." 'e"Hassan S. Bakouch, Journal of Applied Statistics, 2012, "There is scarcely a standard technique that the reader will find left out ... this book is highly recommended for those requiring a ready introduction to applicable methods in time series and serves as a useful resource for pedagogical purposes." --International Statistical Review (2014), 82 "Current time series theory for practice is well summarized in this book." --Emmanuel Parzen, Texas A&M University "What an extraordinary range of topics covered, all very insightfully. I like [the authors'] innovations very much, such as the AR factor table." --David Findley, U.S. Census Bureau (retired) "... impressive coverage of the scope of time series analysis in both frequency and time domain ... One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. ... I commend the authors for having included a number of topics on nonstationary processes ... an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. ... the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book ..." --Hernando Ombao, Journal of the American Statistical Association, March 2013 "The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book's material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis." --Hassan S. Bakouch, Journal of Applied Statistics, 2012, "Current time series theory for practice is well summarized in this book." e"Emmanuel Parzen, Texas A&M University "What an extraordinary range of topics covered, all very insightfully. I like [the authorse(tm)] innovations very much, such as the AR factor table." e"David Findley, U.S. Census Bureau (retired) "e impressive coverage of the scope of time series analysis in both frequency and time domain e One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. e I commend the authors for having included a number of topics on nonstationary processes e an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. e the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book e" e"Hernando Ombao, Journal of the American Statistical Association, March 2013 "The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The booke(tm)s material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis." e"Hassan S. Bakouch, Journal of Applied Statistics, 2012, "… impressive coverage … One unique feature of the book is the emphasis on factoring the AR polynomial function and its roots. … an excellent textbook to adopt for a class and a good introductory book for a student who wants to embark on dissertation research in time series. … the book provides the reader with very good background material to be able to conduct practical and insightful data analysis and be able to comprehend the more theory-oriented books. There are many very good exercises in this book …" -Hernando Ombao, Journal of the American Statistical Association, March 2013 "The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book's material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis." -Hassan S. Bakouch, Journal of Applied Statistics, 2012, The book contains many illustrative examples, theorems with proofs, and applied and theoretical problems at the end of each chapter with real-life applications. Also, the book looks at generating realisations of the mentioned time series models via software packages such as GW-WINKS and R. The book's material is very valuable and is well presented, so it represents a good reference at both undergraduate and postgraduate levels, and also a good source for all who are interested in time series analysis. -Hassan S. Bakouch, Journal of Applied Statistics, 2012
Table of Content
Stationary Time Series Time Series Stationary Time Series Autocovariance and Autocorrelation Functions for Stationary Time Series Estimation of the Mean, Autocovariance, and Autocorrelation for Stationary Time Series Power Spectrum Estimating the Power Spectrum and Spectral Density for Discrete Time Series Time Series Examples Linear Filters Introduction to Linear Filters Stationary General Linear Processes Wold Decomposition Theorem Filtering Applications ARMA Time Series Models Moving Average Processes Autoregressive Processes Autoregressive-Moving Average Processes Visualizing Autoregressive Components Seasonal ARMA(p,q)x(Ps,Qs)sModels Generating Realizations from ARMA(p,q) Processes Transformations Other Stationary Time Series Models Stationary Harmonic Models ARCH and GARCH Models Nonstationary Time Series Models Deterministic Signal-Plus-Noise Models ARIMA(p,d,q) and ARUMA(p,d,q) Models Multiplicative Seasonal ARUMA(p,d,q) x (Ps,Ds,Qs)sModel Random Walk Models G-Stationary Models for Data with Time-Varying Frequencies Forecasting Mean Square Prediction Background Box-Jenkins Forecasting for ARMA(p,q) Models Properties of the Best Forecast Xto(l) pi-Weight Form of the Forecast Function Forecasting Based on the Difference Equation Eventual Forecast Function Probability Limits for Forecasts Forecasts Using ARUMA(p,d,q) Models Forecasts Using Multiplicative Seasonal ARUMA Models Forecasts Based on Signal-plus-Noise Models Parameter Estimation Introduction Preliminary Estimates Maximum Likelihood Estimation of ARMA( p,q) Parameters Backcasting and Estimating σ2a Asymptotic Properties of Estimators Estimation Examples Using Data ARMA Spectral Estimation ARUMA Spectral Estimation Model Identification Preliminary Check for White Noise Model Identification for Stationary ARMA Models Model Identification for Nonstationary ARUMA(p,d,q) Models Model Identification Based on Pattern Recognition Model Building Residual Analysis Stationarity versus Nonstationarity Signal-plus-Noise versus Purely Autocorrelation-Driven Models Checking Realization Characteristics Comprehensive Analysis of Time Series Data: A Summary Vector-Valued (Multivariate) Time Series Multivariate Time Series Basics Stationary Multivariate Time Series Multivariate (Vector) ARMA Processes Nonstationary VARMA Processes Testing for Association between Time Series State-Space Models Proof of Kalman Recursion for Prediction and Filtering Long-Memory Processes Long Memory Fractional Difference and FARMA Models Gegenbauer and GARMA Processes k-Factor Gegenbauer and GARMA Models Parameter Estimation and Model Identification Forecasting Based on the k-Factor GARMA Model Modeling Atmospheric CO2Data Using Long-Memory Models Wavelets Shortcomings of Traditional Spectral Analysis for TVF Data Methods That Localize the ''Spectrum'' in Time Wavelet Analysis Wavelet Packets Concluding Remarks on Wavelets Appendix: Mathematical Preliminaries for This Chapter G-Stationary Processes Generalized-Stationary Processes M-Stationary Processes G(λ)-Stationary Processes Linear Chirp Processes Concluding Remarks Index
