- Title
- A Bayesian analysis of a regime switching volatility model
- Creator
- Livingston Jr, Glen
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2017
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Non-linear time series data is often generated by complex systems. While linear models provide a good first approximation of a system, often a more sophisticated non-linear model is required to properly account for the features of such data. Correctly accounting for these features should lead to the fitting of a more appropriate model. Determining the features exhibited by a particular data set is a difficult task, particularly for inexperienced modellers. Therefore, it is important to move towards a modelling paradigm where little to no user input is required, in order to open statistical modelling to users less experienced in MCMC. This sort of modelling process requires a general class of models that is able to account for the features found in most linear and non-linear data sets. One such class is the STAR-GARCH class of models. These are reasonably general models that permit regime changes in the conditional mean and allow for changes in the conditional covariance. In this thesis, we develop original algorithms that combine the tasks of parameter estimation and model selection for univariate and multivariate STAR-GARCH models. The model order of the conditional mean and the model index of the conditional covariance equation are included as parameters for the model requiring estimation. Combining the tasks of parameter estimation and model selection is facilitated through the Reversible Jump MCMC methodology. Other MCMC algorithms employed for the posterior distribution simulators are the Gibbs sampler, Metropolis-Hastings, Multiple-Try Metropolis and Delayed Rejection Metropolis-Hastings algorithms. The posterior simulation algorithms are successfully implemented in the statistical software program R, and their performance is tested in both extensive simulation studies and practical applications to real world data. The current literature on multivariate extensions of STAR, GARCH, and STAR-GARCH models is quite limited from a Bayesian perspective. The implementation of a set of estimation algorithms that not only provide parameter estimates but is also able to automatically fit the model with highest posterior probability is a significant and original contribution. The impact of such a contribution will hopefully be a step forward on the path towards the automation of time series modelling.
- Subject
- multivariate non-linear time series; STAR; GARCH; Bayesian; reversible jump MCMC; Metropolis-Hastings; Gibbs sampler; delayed rejection; VAR; M-GARCH
- Identifier
- http://hdl.handle.net/1959.13/1342483
- Identifier
- uon:28972
- Rights
- Copyright 2017 Glen Livingston Jr
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 4 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 438 KB | Adobe Acrobat PDF | View Details Download |