A state space model approach to functional time series and time series driven by differential equations

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OF THE DISSERTATION A State Space Model Approach to Functional Time Series and Time Series Driven by Differential Equations by Jiabin Wang Dissertation Director: Professor Rong Chen This dissertation studies the modeling of time series driven by unobservable processes using state space model. New models and methodologies are proposed and applied on a variety of real life examples arising from finance and biology. More specifically, we mainly consider two types of time series: partially observed dynamic systems driven by differential equations and functional time series driven by its feature process. The first type of time series data is generated by a hidden dynamic process controlled by some underlying differential equation with a set of unknown parameters. We propose a state space approach to fit these models with observation data, which is only available at sparsely separated time points as well as with measurement error, and estimate the corresponding parameters. More specifically, we approximate the target nonlinear deterministic/stochastic differential equations by difference equations and convert the dynamic into a state space model(SSM), which is further calibrated by the likelihood calculated from the filtering scheme. The first application converts the HIV dynamic into a linear SSM and estimates all HIV viral dynamic parameters successfully without many constraints. The second application focus on the well-studied ecological SIR model. An efficient filtering scheme is proposed to overcome the difficulty caused by the sparsity of the observed data. The methodology is illustrated and evaluated in the