Modeling, Computation, and Inference
Chapman and Hall/CRC – 2011 – 368 pages
Focusing on Bayesian approaches and computations using simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers.
The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB® code, and other material are available on the authors’ websites.
Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.
The authors systematically develop a state-of-the-art analysis and modeling of time series. … this book is well organized and well written. The authors present various statistical models for engineers to solve problems in time series analysis. Readers no doubt will learn state-of-the-art techniques from this book.
—Hsun-Hsien Chang, Computing Reviews, March 2012
My favorite chapters were on dynamic linear models and vector AR and vector ARMA models.
—William Seaver, Technometrics, August 2011
… a very modern entry to the field of time-series modelling, with a rich reference list of the current literature, including 85 references from 2008 and later. It is well-written and I spotted very few typos. This textbook can undoubtedly work as a reference manual for anyone entering the field or looking for an update. … I am certain there is more than enough material within Time Seriesto fill an intense one-semester course.
—International Statistical Review (2011), 79
Notation, Definitions, and Basic Inference
Problem areas and objectives
Stochastic processes and stationarity
Autocorrelation and cross-correlation functions
Smoothing and differencing
A primer on likelihood and Bayesian inference
Traditional Time Domain Models
Structure of autoregressions
Estimation in autoregressive (AR) models
Further issues on Bayesian inference for AR models
Autoregressive moving average (ARMA) models
The Frequency Domain
Some spectral theory
Discussion and extensions
Dynamic Linear Models
General linear model structures
Forecast functions and model forms
Inference in dynamic linear models (DLMs): basic normal theory
Extensions: non-Gaussian and nonlinear models
Posterior simulation: Markov chain Monte Carlo (MCMC) algorithms
State-Space Time-Varying Autoregressive Models
Time-varying autoregressions (TVAR) and decompositions
TVAR model specification and posterior inference
Sequential Monte Carlo Methods for State-Space Models
General state-space models
Posterior simulation: sequential Monte Carlo (SMC)
Mixture Models in Time Series
Markov switching models
Mixtures of general state-space models
Case study: detecting fatigue from EEGs
Univariate stochastic volatility models
Topics and Examples in Multiple Time Series
Multichannel modeling of EEG data
Some spectral theory
Dynamic lag/lead models
Vector AR and ARMA Models
Vector AR (VAR) models
Vector ARMA (VARMA) models
Estimation in VARMA
Extensions: mixtures of VAR processes
Multivariate DLMs and Covariance Models
Theory of multivariate and matrix normal DLMs
Multivariate DLMs and exchangeable time series
Learning cross-series covariances
Time-varying covariance matrices
Multivariate dynamic graphical models
Problems appear at the end of each chapter.
Raquel Prado is an associate professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz.
Mike West is the Arts & Sciences Professor of Statistical Science in the Department of Statistical Science at Duke University.