Mathematical Sciences: Statistical Methods for Nonlinear Inference in Time Series with Stochastic Variance

建议：DMS 9505109 PI：尼克·波尔森研究所：芝加哥大学标题：具有随机方差的时间序列中非线性推断的统计方法摘要：该项目开发并将非线性推断问题的分层统计模型应用于具有随机方差和非正态误差的多变量数据的新领域。Jquier，Polson和Rossi(1994)以前的研究表明，对于正态单变量随机方差的情况，这种方法比通常的统计方法，如广义矩方法要好。本研究利用马尔可夫链、蒙特卡罗技术和分层建模技术，构建并实现了一种综合了多变量、随机方差和非正态分布的推理方法。在这种方法中，很容易检查替代假设的影响，例如不同的误差分布对结果推断的影响。此外，该项目还开发了一种在存在随机方差的情况下使用的异常值诊断程序。这项研究开发了一种分析时间序列数据的一般方法，如股票价格、利率和其他金融序列，其中方差或波动性随着时间的推移而变化。直到最近，这些数据都是在假设方差不变或方差根据预定模式变化的情况下分析的。最近的统计工作表明，分析这些数据的更好方法是假设随机变化的方差。这种方法被称为随机方差(或波动性)时间序列建模。这项研究为分析这些模型提供了一个更一般的框架，它不依赖于现有方法通常的限制性假设。提供了一些统计工具来分析随机方差框架内的数据。本研究所发展的方法论提出了一种改进的时间序列数据分析方法，并包括了几个基于金融时间序列的L例子。

Proposal: DMS 9505109 PI: Nick Polson Institution: University of Chicago Title: Statistical Methods for Nonlinear Inference in Time Series with Stochastic Variance Abstract: This project develops and applies hierarchical statistical models for nonlinear inference problems to the new areas of multivariate data with stochastic variance as well as nonnormal errors. Previous research by Jacquier, Polson and Rossi (1994) has shown that this methodology is better than the usual statistical methods, such as generalized methods of moments, for the case of normal univariate stochastic variance. This research utilizes Markov chain Monte Carlo techniques and hierarchical modeling to construct and implement a methodology for inference which incorporates multivariate stochastic variance and nonnormality. Within this methodology, it is straightforward to examine the effects of alternative assumptions such as different error distributions on the resulting inferences. In addition, the project develops an outlier diagnostic procedure to be used in the presence of stochastic variance. This research develops a general methodology for analyzing time series data, such as stock prices, interest rates and other financial series, where variance, or volatility, changes over time. Until recently, such data were analyzed assuming either constant variance or variance changing according to a predetermined pattern. Recent statistical work has shown that a better way of analyzing these data is to assume randomly changing variance. This approach is known as stochastic variance (or volatility) time series modeling. This research provides a more general framework for analyzing these models which does not rely on the usual limiting assumptions of existing methodologies. A number of statistical tools are provided to analyze the data within the stochastic variance framework. The methodology developed in this research presents an improved way to analyze time series data, and severa l examples based on financial time series are included.