Physical Sciences and Mathematics Commons^™

Prediction Intervals For Fractionally Integrated Time Series And Volatility Models, Rukman Ekanayake

Doctoral Dissertations

"The two of the main formulations for modeling long range dependence in volatilities associated with financial time series are fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) and hyperbolic generalized autoregressive conditional heteroscedastic (HYGARCH) models. The traditional methods of constructing prediction intervals for volatility models, either employ a Gaussian error assumption or are based on asymptotic theory. However, many empirical studies show that the distribution of errors exhibit leptokurtic behavior. Therefore, the traditional prediction intervals developed for conditional volatility models yield poor coverage. An alternative is to employ residual bootstrap-based prediction intervals. One goal of this dissertation research is to develop …

Integrating Snp Data And Imputation Methods Into The Dna Methylation Analysis Framework, Yuqing Su

Doctoral Dissertations

"DNA methylation is a widely studied epigenetic modification that can influence the expression and regulation of functional genes, especially those related to aging, cancer and other diseases. The common goal of methylation studies is to find differences in methylation levels between samples collected under different conditions. Differences can be detected at the site level, but regulated methylation targets are most commonly clustered into short regions. Thus, identifying differentially methylated regions (DMRs) between different groups is of prime interest. Despite advanced technology that enables measuring methylation genome-wide, misinterpretations in the readings can arise due to the existence of single nucleotide polymorphisms …

Count Data Time Series Models And Their Applications, Yi Zhang

Doctoral Dissertations

“Due to fast developments of advanced sensors, count data sets have become ubiquitous in many fields. Modeling and forecasting such time series have generated great interest. Modeling can shed light on the behavior of the count series and to see how they are related to other factors such as the environmental conditions under which the data are generated. In this research, three approaches to modeling such count data are proposed.

First, a periodic autoregressive conditional Poisson (PACP) model is proposed as a natural generalization of the autoregressive conditional Poisson (ACP) model. By allowing for cyclical variations in the parameters of …

Modeling Time Series With Conditional Heteroscedastic Structure, Ratnayake Mudiyanselage Isuru Panduka Ratnayake

Doctoral Dissertations

"Models with a conditional heteroscedastic variance structure play a vital role in many applications, including modeling financial volatility. In this dissertation several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroscedastic model, are further generalized to provide more effective modeling of price range data well as count data. First, the Conditional Autoregressive Range (CARR) model is generalized by introducing a composite range-based multiplicative component formulation named the Composite CARR model. This formulation enables a more effective modeling of the long and short-term volatility components present in price range data. It treats the long-term volatility as a stochastic component that in …