Models for Dependent Time Series: 1st Edition (Hardback) book cover

Models for Dependent Time Series

1st Edition

By Granville Tunnicliffe Wilson, Marco Reale, John Haywood

Chapman and Hall/CRC

340 pages | 149 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781584886501
pub: 2015-07-29
SAVE ~$19.59
eBook (VitalSource) : 9780429144400
pub: 2015-07-29
from $46.98

FREE Standard Shipping!


Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data.

The first four chapters discuss the two main pillars of the subject that have been developed over the last 60 years: vector autoregressive modeling and multivariate spectral analysis. These chapters provide the foundational material for the remaining chapters, which cover the construction of structural models and the extension of vector autoregressive modeling to high frequency, continuously recorded, and irregularly sampled series. The final chapter combines these approaches with spectral methods for identifying causal dependence between time series.

Web Resource

A supplementary website provides the data sets used in the examples as well as documented MATLAB® functions and other code for analyzing the examples and producing the illustrations. The site also offers technical details on the estimation theory and methods and the implementation of the models.


"This book covers the three important pillars of multiple time series—vector autoregressive modeling, spectral analysis, and graphical models—a useful characteristic for a modern book on time series since each brings new insights to the analyses and each has the ability to complement the other. The book is well-written and should be accessible to anyone with a good understanding of multiple linear regression…the authors are successful in communicating concepts central to modeling time series in the time and frequency domain as well as using the graphical modeling approach. The numerous examples used to illustrate techniques covered in the chapters are easy to follow and this makes the book very useful…The choice of content for the chapters as well as the references for topics covered in the book is excellent…it is a valuable addition to the literature on time series analysis."

—Swati Chandna, University College London, The American Statistician, November 2016

"This book is a valuable contribution to researchers and students working with time series with emphasis on multivariate time series including both the time domain and frequency domain approaches. The presentation is accessible to students with intermediate undergraduate level courses in regression analysis and time series analysis. There is an emphasis on basic principles with many unique insightful approaches such as the introduction of frequency domain thinking using harmonic contrasts and many other such insights…this book contains a wealth of fascinating multivariate time series ranging from applications in finance, economics, management science, ecology, manufacturing, climate change and biology. The authors provide a website ( where data and computer software can be downloaded or contributed by interested researchers."

Journal of Time Series Analysis, June 2016

"I enjoyed reading this book. It is like no other text on multivariate time series and contains a lot of modern material not found elsewhere. Chapters 1-4 take a look at the historical treatment of multivariate time series, not dwelling on theory, but concentrating on applications and intuitive motivation. The remaining chapters comprise work done mainly by the authors in the last 20 years, introducing and integrating concepts, such as graphical modeling, using directed acyclic graphs and a vector version of the ZAR models, which they have invented, developed, and applied. There are also chapters on continuous time and irregularly sampled time series. Throughout, the accent is on application, and the book is thus suitable for a broader audience than existing, more theoretical texts. Indeed, the book should be accessible to anyone modeling multivariate time series. MATLAB code and other explanations are to be made available to complement the text."

Barry Quinn, Professor of Statistics, Macquarie University, Australia

Table of Contents

Introduction and overview

Examples of time series

Dependence within and between time series

Some of the challenges of time series modeling

Feedback and cycles

Challenges of high frequency sampling

Causal modeling and structure

Some practical considerations

Lagged regression and autoregressive models

Stationary discrete time series and correlation

Autoregressive approximation of time series

Multi-step autoregressive model prediction

Examples of autoregressive model approximation

The multivariate autoregressive model

Autoregressions for high lead time prediction

Model impulse response functions

The covariances of the VAR model

Partial correlations of the VAR model

Inverse covariance of the VAR model

Autoregressive Moving Average models

State space representation of VAR models

Projection using the covariance matrix

Lagged response functions of the VAR model

Spectral analysis of dependent series

Harmonic components of time series

Cycles and lags

Cycles and stationarity

The spectrum and cross-spectra of time series

Dependence between harmonic components

Bivariate and multivariate spectral properties

Estimation of spectral properties

Sample covariances and smoothed spectrum

Tapering and pre-whitening

Practical examples of spectral analysis

Harmonic contrasts in large samples

The estimation of vector autoregressions

Methods of estimation

The spectrum of a VAR model

Yule–Walker estimation of the VAR(p) model

Estimation of the VAR(p) by lagged regression

Maximum likelihood estimation, MLE

VAR models with exogenous variables, VARX

The Whittle likelihood of a time series model

Graphical modeling of structural VARs

The structural VAR, SVAR

The directed acyclic graph, DAG

The conditional independence graph, CIG

Interpretation of CIGs

Properties of CIGs

Estimation and selection of DAGs

Building a structural VAR, SVAR

Properties of partial correlation graphs

Simultaneous equation modeling

An SVAR model for the Pig market: the innovations

A full SVAR model of the Pig market series

VZAR: an extension of the VAR model

Discounting the past

The generalized shift operator

The VZAR model

Properties of the VZAR model

Approximating a process by the VZAR model

Yule–Walker fitting of the VZAR

Regression fitting of the VZAR

Maximum likelihood fitting of the VZAR

VZAR model assessment

Continuous time VZAR models

Continuous time series

Continuous time autoregression and the CAR(1)

The CAR(p) model

The continuous time generalized shift

The continuous time VZAR model, VCZAR

Properties of the VCZAR model

Approximating a continuous process by a VCZAR

Yule–Walker fitting of the VCZAR model

Regression and ML estimation of the VCZAR

Irregularly sampled series

Modeling of irregularly sampled series

The likelihood from irregularly sampled data

Irregularly sampled univariate series models

The spectrum of irregularly sampled series

Recommendations on VCZAR model selection

A model of regularly sampled bivariate series

A model of irregularly sampled bivariate series

Linking graphical, spectral and VZAR methods

Outline of topics

Partial coherency graphs

Spectral estimation of causal responses

The structural VZAR, SVZAR

Further possible developments


Subject Index

Author Index

About the Authors

Granville Tunnicliffe Wilson is a reader emeritus in the Department of Mathematics and Statistics at Lancaster University, UK. His research focuses on methodology and software for time series modeling and prediction.

Marco Reale is an associate professor in the School of Mathematics and Statistics at the University of Canterbury, New Zealand. His research interests include time series analysis, statistical learning, and stochastic optimization.

John Haywood is a senior lecturer in the School of Mathematics and Statistics at Victoria University of Wellington, New Zealand. His research interests include time series analysis, seasonal modeling, and statistical applications, particularly in ecology.

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

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