Thesis Defense - Shi

Many of the traditional models used in time series analysis are global models, such as regressions and neural networks. This dissertation develops a class of structural time series models using local models with the assumption that the observed time series depends on hidden states. Two models have been proposed based on Markov processes and mixtures. One is Markov Gated Experts where the underlying process is assumed to be observable; the other is Hidden Markov Experts where the underlying process is assumed unobservable. This thesis includes both theoretical and empirical analysis of these methods. The studies lead to understanding the behavior of the models and possible applications of these models in different areas, such as financial time series analysis.

Results from both the real world data and computer generated data support similar conclusions. Markov Gated Experts are applied to analyze the nonlinear, low-noise laser data. Hidden Markov Experts are used to predict the conditional density of time series. It is applied to model both high frequency foreign exchange data and daily Standard & Poor 500 data. The hidden regimes retrieved by Hidden Markov Experts correspond to the volatility clustering. Both models have better generalization than global linear models (e.g. linear regression models) and global nonlinear models (e.g. neural networks).