Time Series: Modeling, Computation, and Inference (Hardback) book cover

Time Series

Modeling, Computation, and Inference

By Raquel Prado, Mike West

© 2011 – Chapman and Hall/CRC

368 pages | 83 B/W Illus.

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About the Book

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

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


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


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


Problems appear at the end of each chapter.

About the Authors

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.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General