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

拟议的研究是一个正在进行的研究计划的一部分，在商业，金融和工业领域的时间序列建模和统计。 建模和预测波动性在评估金融市场的风险和不确定性方面发挥着重要作用。我们引入了一类新的波动率模型，称为伽马随机波动率（GSV）模型。本研究计划的第一个目标是进一步发展这种方法和传统的随机波动率模型，设计有效的方法来估计它们，检查它们的充分性，并生成预测。我们计划使用最优二次估计函数（QEF）来估计模型的参数。我们还为非负时间序列引入了乘积自回归模型，并计划将其应用于波动性模型。 第二个目标是发展在公共卫生、空气污染和金融等领域具有广泛应用的计数时间序列模型。在空气污染研究中，模拟由颗粒物（如灰尘和烟雾）以及气味和噪声引起的烦恼，观察结果通常是计数，并且随时间而变化，导致可能使用具有泊松或其他离散边缘分布的计数时间序列模型。在某些情况下，这些时间序列中的一些，例如医院中罕见疾病或地区犯罪的每月计数可能包含大量的零，这需要使用所谓的零通货膨胀模型。因此，我们可以使用具有零通货膨胀泊松边缘分布的特殊计数时间序列模型。在这些计数模型中，均值和方差可能取决于先前的测量值，因此很自然地考虑这些参数的广义自回归条件异方差（GARCH）类模型或随机波动率类型模型。另一个目标是开发用于指定这些模型的方法，估计它们，检查适当性，并生成预测。 政策决策和各种环境法规的实施需要来自适当收集和分析的数据的准确信息。第四个目标是设计新的程序来处理异常值和长记忆，这是经常遇到的空气污染和水质时间序列。质量改进工作对于加拿大商业和工业组织的成功非常重要。该项目的第五个目标是制定新的统计方法，并加强可适用于加拿大工商业的现有方法。我们计划开发工业建模的经验似然程序，设计中的性能指标的自举分析，以及在可能包含离群值的时间序列数据的背景下进行多变量预测的降维方法。

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.