Models for dependent time series

Table of Contents:

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Linking graphical, spectral and VZAR methods

• Outline of topics
• Partial coherency graphs
• Spectral estimation of causal responses
• The structural VZAR, SVZAR
• Further possible developments

References

Subject Index

Author Index

Models for Dependent Time Series address 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.


(https://www.crcpress.com/Models-for-Dependent-Time-Series/Wilson-Reale-Haywood/9781584886501)