Non-Gaussian Times Series Modeling with Applications in Finance, Dealing with Outliers and Long Memory and Process Improvement.

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The proposed research is part of an ongoing research program in the areas of Time Series Modeling and Statistics in Business, Finance, and Industry.***Modeling and predicting volatility play an important role in assessing risk and uncertainty in financial markets. We had introduced a new class of volatility models known as Gamma Stochastic Volatility (GSV) models. The first objective in this research program is to develop further this approach and the traditional stochastic volatility models, devise efficient methods of estimating them, check for their adequacy, and generate predictions. We plan to use optimal Quadratic Estimating Functions (QEF) for estimating the parameters of the models. We had also introduced product auto-regressive models for non-negative time series and we plan to adapt these to model volatility. ***The second objective is to develop the area of count time series models which has wide applications in areas such as public health, air pollution, and finance. In air pollution studies, modeling annoyance caused by particulate matter such as dust and smoke and by odor and noise the observations are often counts and are dependent over time leading to the possible use of count time series models with Poisson or other discrete marginal distributions. In some cases, some of these time series such as monthly counts of a rare disease in a hospital or crimes in a region may contain large numbers of zeros which requires the use of what is known as zero inflation models. Thus we may use special count time series models with zero inflation Poisson marginal distributions. In these count models, the mean and variance may depend on the previous measurements and so it is natural to consider generalized auto-regressive conditional heteroscadastic (GARCH) like models or Stochastic Volatility type models for such parameters. Another objective is to develop methods for specifying these models, estimating them, checking for adequacy, and generating predictions.***Policy decisions and the implementation of various environmental regulations require accurate information from appropriately collected and analyzed data. A fourth objective is to devise new procedures to deal with outliers and long memory which are often encountered in air pollution and water quality time series. Quality Improvement efforts are very important for the success of Canadian Business and Industrial organizations. A fifth objective of the project is to develop new statistical methods and enhance existing ones which can be applied to Canadian Business and Industry. We plan to develop empirical likelihood procedures for industrial modeling, bootstrap analysis of performance measures in designs and dimension reduction methods for multivariate prediction in the context of time series data which may contain outliers.**