Date of Award

Summer 2013

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Computational and Applied Mathematics

Committee Director

Norou Diawara

Committee Member

Larry Filer

Committee Member

Nak-Kyeong Kim

Committee Member

Cynthia M. Jones


Stochastic processes have applications in many areas such as oceanography and engineering. Special classes of such processes deal with time series of sparse data. Studies in such cases focus in the analysis, construction and prediction in parametric models. Here, we assume several non-linear time series with additive noise components, and the model fitting is proposed in two stages. The first stage identifies the density using all the clusters information, without specifying any prior knowledge of the underlying distribution function of the time series. The effect of covariates is controlled by fitting the linear regression model with serially correlated errors. In the second stage, we partition the time series into consecutive non-overlapping intervals of quasi stationary increments where the coefficients shift from one stable regression relationship to a different one using a breakpoints detection algorithm. These breakpoints are estimated by minimizing the likelihood from the residuals. We approach time series prediction through the mixture distribution of combined error components. Parameter estimation of mixture distribution is done by using the EM algorithm. We apply the method to fish otolith data influenced by various environmental conditions and get estimation of parameters for the model.