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.