Change-point stochastic regression models with applications to econometric time series

Motivated by applications of stochastic regression models to econometric time series, this thesis introduces a class of hidden Markov models for regression with stochastic regressors, in which the regression parameters and/or error covariance matrices may undergo abrupt changes at unknown times while staying constant between two adjacent change-points. Besides capturing certain key features of typical econometric time series undergoing occasional structural changes, the proposed models are also computationally and analytically tractable because they involve standard conjugate priors and a simple renewal process for the occurrence of change-points. Explicit formulas are available for recursive representations of optimal filters and smoothers for the regression parameters and error covariance matrices. The computational complexity of the recursive updates for the optimal filters, however, grows to infinity with the number of observations. Bounded-complexity approximations to the Bayes estimates are developed that have much lower computational complexity and yet are comparable to the Bayes estimates in statistical efficiency. The problem of unknown hyperparameters is also addressed. Simulation studies and a case study in financial time series are provided, and further extensions and applications are discussed.