Tunnicliffe Wilson / Reale / Haywood Models for Dependent Time Series

Erscheinungsjahr 2015
ISBN: 978-1-4200-1150-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 340 Seiten

Reihe: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

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.

Zielgruppe

Researchers and graduate students in statistics, econometrics, finance, marketing, biometrics, and environmetrics.

Autoren/Hrsg.

Tunnicliffe Wilson, Granville

Reale, Marco

Haywood, John

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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 (ML) estimation

VAR models with exogenous variables, VARX

The Whittle likelihood of a time series model

Graphical modeling of structural VARs

The structural VAR

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: the CAR()

The CAR(p) model

The continuous time generalized shift

VCZAR: the continuous time VZAR model

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

Bibliography

Subject Index

Author Index

Über Autor(innen)

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.