Dynamic Bayesian smooth transition autoregressive (DBSTAR) models for non-stationary nonlinear time series

dos Santos, Alexandre Jose (2014). Dynamic Bayesian smooth transition autoregressive (DBSTAR) models for non-stationary nonlinear time series. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f836

Abstract

In this thesis, Dynamic Bayesian Smooth Transition Autoregressive (DBSTAR) models are proposed for nonlinear time series, as an alternative to both the classical Smooth Transition Autoregressive (STAR) models and Computational Bayesian STAR (CBSTAR) models. DBSTAR models are autoregressive formulations of dynamic linear models based on polynomial approximations of transition functions of STAR models. Unlike classical STAR and CBSTAR models, their parameters vary in time, being suitable for modelling both global and local non-stationary processes. Since DBSTAR models are Bayesian, the models do not require extensive historical data for parametric estimation and allow expert intervention via prior distribution assessment of model parameters. Because they are analytical and sequential, DBSTAR models, respectively, avoid potential computational problems associated with CBSTAR models, such as convergence issues, and allow fast estimation of dynamic parameters sequentially in time, being thus suitable for real time applications. Proposed DBSTAR models have been applied to two data sets: the much used Canadian Lynx data set, in which the aim is to validate DBSTAR models by comparing their fitting performances with existing approaches in the literature, and a Brazilian electricity load data set, for which existing models are not suitable.