Time Series

Modeling, Computation, and Inference, Second Edition

Raquel Prado, Marco A. R. Ferreira, Mike West

• Publisher: Chapman and Hall/CRC
• Year: 2021
• ISBN:
  9781498747059
• Edition: 2
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Focusing on Bayesian approaches and computations using analytic and simulation-based methods for inference, Time Series: Modeling, Computation, and Inference, Second Edition 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, analysis and forecasting, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and contacts research frontiers in multivariate time series modeling and forecasting.

It presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. It explores the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian formulations and computation, including use of computations based on Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. It illustrates the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, environmental science, and finance.

Along with core models and methods, the book represents state-of-the art approaches to analysis and forecasting in challenging time series problems. It also demonstrates the growth of time series analysis into new application areas in recent years, and contacts recent and relevant modeling developments and research challenges.

New in the second edition:

• Expanded on aspects of core model theory and methodology.

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• Multiple new examples and exercises.

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• Detailed development of dynamic factor models.

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• Updated discussion and connections with recent and current research frontiers.

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Chapter 1

Notation, definitions, and basic inference

This chapter discusses key goals of time series analysis with motivating examples from different applied areas. Notation and key concepts related to time series processes are introduced, including the characterizationof stationary processes. This is followed by a brief review on likelihood and Bayesian modeling and inference tools, which includes a primer on simulation-based methods for posterior inference within the Bayesian framework. The modeling and inference tools are illustrated for the class offirst-order autoregressive processes.

1.1 Problem Areas and Objectives

The expression time series data, or time series, usually refers to a set of observations collected sequentially in time. These observations could have been collected at equally spaced time points. In this case we use the notation y_t with $(t=\dots ,-1,0,1,2,\dots )$; i.e., the set of observations is indexed by t, the time at which each observation was taken. If the observations were not taken at equally spaced points, then we use the notation $y_{t_i}$, with $i=1,2,\dots$.

A time series process is a stochastic process or a collection of random variables y_t indexed in time. Note that y_t will be used throughout the book to denote a random variable or an actual realization of the time series process at time t. We use the notation $\{y_t,t\in \mathcal{T}\},$ or simply $\left\{y_t\right\}$, to refer to the time series process. If $\mathcal{T}$ is of the form $\{t_i,i\in \mathbb{N}\}$, with ℕ the natural numbers, then the process is a discrete-time random process, and if $\mathcal{T}$ is an interval in the real line, or a collection of intervals in the real line, then the proces...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• Authors
• 1 Notation, definitions, and basic inference
• 2 Traditional time domain models
• 3 The frequency domain
• 4 Dynamic linear models
• 5 State-space TVAR models
• 6 SMC methods for state-space models
• 7 Mixture models in time series
• 8 Topics and examples in multiple time series
• 9 Vector AR and ARMA models
• 10 General classes of multivariate dynamic models
• 11 Latent factor models
• Bibliography
• Author Index
• Subject Index