Autoregressive models with time-varying parameters and applications to financial time series

Volatility estimation is the cornerstone of empirical finance, as portfolio theory, asset pricing, and hedging all involve volatility. Popular approaches to modeling volatility include the ARCH process and SV model. However, there are shortcomings of such models as a description of the volatility of asset returns. Recent attempts to address these shortcomings involve introducing an unobserved Markov Chain to the parameters of ARCH and SV models.; This dissertation presents a new promising alternative to modeling asset returns and volatility, namely, a change-point autoregressive model in which the autoregressive coefficients and error variances may undergo abrupt changes at unknown time points, staying constant between adjacent change points. Utilizing conjugate priors, we derive the recursive closed-form Bayes estimates of these parameters. Approximations to the Bayes solution are developed which have much lower computational complexity and yet are comparable to the Bayes estimates in statistical efficiency. We also address the problem of handling unknown hyperparameters and propose a practical method for simultaneous estimation of hyperparameters together with model parameters. The method is based on the accumulated prediction error criterion and can be conveniently implemented by parallel recursive algorithms. Our results are applied to modeling stock returns and their volatility by using real financial data which show possible structural changes in both the returns and volatility.