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Time Series Modeling, Inference and Forecasting

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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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