Description
Taylor & Francis Ltd Time Series 2010 Edition by Raquel Prado, Mike West
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 (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. Notation, Definitions, and Basic InferenceProblem areas and objectives Stochastic processes and stationarity Autocorrelation and cross-correlation functions Smoothing and differencing A primer on likelihood and Bayesian inferenceTraditional Time Domain ModelsStructure of autoregressionsForecasting Estimation in autoregressive (AR) modelsFurther issues on Bayesian inference for AR modelsAutoregressive moving average (ARMA) modelsOther modelsThe Frequency DomainHarmonic regressionSome spectral theoryDiscussion and extensionsDynamic Linear ModelsGeneral linear model structures Forecast functions and model formsInference in dynamic linear models (DLMs): basic normal theoryExtensions: non-Gaussian and nonlinear models Posterior simulation: Markov chain Monte Carlo (MCMC) algorithmsState-Space Time-Varying Autoregressive ModelsTime-varying autoregressions (TVAR) and decompositionsTVAR model specification and posterior inferenceExtensionsSequential Monte Carlo Methods for State-Space ModelsGeneral state-space models Posterior simulation: sequential Monte Carlo (SMC)Mixture Models in Time SeriesMarkov switching models Multiprocess models Mixtures of general state-space models Case study: detecting fatigue from EEGs Univariate stochastic volatility modelsTopics and Examples in Multiple Time SeriesMultichannel modeling of EEG data Some spectral theory Dynamic lag/lead models Other approachesVector AR and ARMA ModelsVector AR (VAR) modelsVector ARMA (VARMA) modelsEstimation in VARMAExtensions: mixtures of VAR processesMultivariate DLMs and Covariance ModelsTheory of multivariate and matrix normal DLMs Multivariate DLMs and exchangeable time series Learning cross-series covariances Time-varying covariance matricesMultivariate dynamic graphical modelsAuthor Index Subject IndexBibliography Problems appear at the end of each chapter.