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

这项拟议的研究是商业、金融和工业中时间序列建模和统计领域正在进行的研究计划的一部分。 建模和预测波动率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，称为伽玛随机波动率(GSV)模型。这个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，并产生预测。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产品自回归模型，我们计划对这些模型进行调整，以适应波动性模型。 第二个目标是发展在公共卫生、空气污染和金融等领域有广泛应用的计数时间序列模型领域。在空气污染研究中，对粉尘和烟雾等颗粒物以及气味和噪声造成的烦扰进行建模，观测结果通常是计数的，并且随着时间的推移而依赖，因此可能使用带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时间序列，例如医院的每月罕见疾病计数或一个地区的犯罪数量，可能包含大量的零，这需要使用所谓的零通胀模型。因此，我们可以使用具有零通胀泊松边际分布的特殊计数时间序列模型。在这些计数模型中，均值和方差可能依赖于先前的测量，因此自然会考虑此类参数的广义自回归条件异方差(GARCH)模型或随机波动率类型模型。另一个目标是开发指定这些模型、估计它们、检查充分性和生成预测的方法。 政策决策和各种环境法规的实施需要从适当收集和分析的数据中获得准确的信息。第四个目标是设计新的程序来处理空气污染和水质时间序列中经常遇到的离群值和长期记忆。质量改进工作对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开发新的统计方法并加强可应用于加拿大工商业的现有方法。我们计划开发用于工业建模的经验似然程序、设计中的绩效衡量的自举分析以及在可能包含异常值的时间序列数据的背景下用于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.