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Time Series Modeling, Inference and Forecasting

Focusing on Bayesian approaches and computations using up-to-date 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(R) 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.
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Table of Contents

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 Forecasting Estimation in autoregressive (AR) models Further issues on Bayesian inference for AR models Autoregressive moving average (ARMA) models Other models The Frequency Domain Harmonic regression 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 Extensions 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 Multiprocess 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 Other approaches 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 Author Index Subject Index Bibliography Problems appear at the end of each chapter.

About the Author

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.


! 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 Series to fill an intense one-semester course. --International Statistical Review (2011), 79

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