Time Series Analysis and Its Applications: With R Examples

by Robert H. Shumway, David S. Stoffer

Overview

This 5th edition of this popular graduate textbook presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. It includes numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The R package ‘astsa’ has had major updates and the text will reflect those updates. In general, the graphics have been improved. New topics include random number generation, modeling and fitting predator-prey interactions, more emphasis on structural models, testing for linearity, discussion of EM algorithm is more extensive, Bayesian analysis of state space models and MCMC is more extensive (including new scripts in astsa), particle methods are introduced, shastic volatility coverage is expanded, changepoint detection is introduced (new topic).

The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, ARMAX models, shastic volatility, and Markov chain Monte Carlo integration methods.

This edition includes R code for each numerical example.

Product Details

ISBN-13:	9783319524528
Publisher:	Springer-Verlag New York, LLC
Publication date:	04/25/2017
Series:	Springer Texts in Statistics
Sold by:	Barnes & Noble
Format:	eBook
File size:	12 MB
Note:	This product may take a few minutes to download.

About the Author

Robert H. Shumway is Professor Emeritus of Statistics at the University of California, Davis. He is a Fellow of the American Statistical Association and a member of the International Statistical Institute. He won the 1986 American Statistical Association Award for Outstanding Statistical Application and the 1992 Communicable Diseases Center Statistics Award; both awards were for joint papers on time series applications. He is also the author of a Prentice-Hall text on applied time series analysis and served as a Departmental Editor for the Journal of Forecasting and Associate Editor for the Journal of the American Statistical Association.

David S. Stoffer is Professor of Statistics at the University of Pittsburgh. He is a Fellow of the American Statistical Association and has made seminal contributions to the analysis of categorical time series. David won the 1989 American Statistical Association Award for Outstanding Statistical Application in a joint paper analyzing categorical time series arising in infant sleep-state cycling. He is currently a Departmental Editor of the Journal of Forecasting and an Associate Editor of the Annals of Statistical Mathematics. He has served as Program Director in the Division of Mathematical Sciences at the National Science Foundation and as Associate Editor for the Journal of the American Statistical Association.

Table of Contents

Characteristics of Time Series     1
Introduction     1
The Nature of Time Series Data     4
Time Series Statistical Models     11
Measures of Dependence: Autocorrelation and Cross-Correlation     18
Stationary Time Series     23
Estimation of Correlation     29
Vector-Valued and Multidimensional Series     34
Problems     40
Time Series Regression and Exploratory Data Analysis     48
Introduction     48
Classical Regression in the Time Series Context     49
Exploratory Data Analysis     57
Smoothing in the Time Series Context     71
Problems     79
ARIMA Models     84
Introduction     84
Autoregressive Moving Average Models     85
Difference Equations     98
Autocorrelation and Partial Autocorrelation Functions     103
Forecasting     110
Estimation     122
Integrated Models for Nonstationary Data     140
Building ARIMA Models     143
Multiplicative Seasonal ARIMA Models     154
Problems     165
Spectral Analysis and Filtering     174
Introduction     174
Cyclical Behavior and Periodicity     176
The Spectral Density     181
Periodogram and Discrete Fourier Transform     187
Nonparametric Spectral Estimation     197
Multiple Series and Cross-Spectra     215
Linear Filters     220
Parametric Spectral Estimation     228
Dynamic Fourier Analysis and Wavelets     232
Lagged Regression Models     245
Signal Extraction and Optimum Filtering     251
Spectral Analysis of Multidimensional Series     256
Problems     258
Additional Time Domain Topics     271
Introduction     271
Long Memory ARMA and Fractional Differencing     271
GARCH Models     280
Threshold Models     289
Regression with Autocorrelated Errors     293
Lagged Regression: Transfer Function Modeling     295
Multivariate ARMAX Models     302
Problems     320
State-Space Models     324
Introduction     324
Filtering, Smoothing, and Forecasting     330
Maximum Likelihood Estimation     339
Missing Data Modifications      348
Structural Models: Signal Extraction and Forecasting     352
ARMAX Models in State-Space Form     355
Bootstrapping State-Space Models     357
Dynamic Linear Models with Switching     362
Nonlinear and Non-normal State-Space Models Using Monte Carlo Methods     376
Stochastic Volatility     388
State-Space and ARMAX Models for Longitudinal Data Analysis     394
Problems     404
Statistical Methods in the Frequency Domain     412
Introduction     412
Spectral Matrices and Likelihood Functions     416
Regression for Jointly Stationary Series     417
Regression with Deterministic Inputs     426
Random Coefficient Regression     434
Analysis of Designed Experiments     438
Discrimination and Cluster Analysis     449
Principal Components and Factor Analysis     464
The Spectral Envelope     479
Problems     496
Large Sample Theory     501
Convergence Modes     501
Central Limit Theorems     509
The Mean and Autocorrelation Functions     513
Time Domain Theory     522
Hilbert Spaces and the Projection Theorem      522
Causal Conditions for ARMA Models     526
Large Sample Distribution of the AR(p) Conditional Least Squares Estimators     528
The Wold Decomposition     532
Spectral Domain Theory     534
Spectral Representation Theorem     534
Large Sample Distribution of the DFT and Smoothed Periodogram     539
The Complex Multivariate Normal Distribution     550
References     555
Index     569

Editorial Reviews

The authors have to be congratulated for their ability to describe in a book of less than 600 pages such a variety of topics and methods, together with scripts allowing the reproduction of the results, for so many real examples. It is a valuable contribution with a strong statistical orientation and a carefully designed pleasant typography.” (Anna Bartkowiak, ISCB News, iscb.info, Issue 65, June, 2018)

“The chapters are nicely structured, well presented and motivated. … it provides sufficient exercise questions making it easier for adoption as a graduate textbook. The book will be equally attractive to graduate students, practitioners, and researchers in the respective fields. … The book contributes stimulating and substantial knowledge for time series analysis for the benefit of a host of community and exhibits the use and practicality of the fabulous subject statistics.” (S. Ejaz Ahmed, Technometrics, Vol. 59 (4), November, 2017)

From the Publisher