Time Series: Modeling, Computation, and Inference (Hardcover)

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.