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

项目编号：DMS 9505109项目发起人：Nick Polson机构：芝加哥大学题目：具有随机方差的时间序列非线性推理的统计方法摘要：本项目开发并将非线性推理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。Jacquier， Polson和Rossi（1994）先前的研究表明，对于正态单变量随机方差，该方法优于通常的统计方法，如广义矩量方法。本研究利用马尔可夫链蒙特卡罗技术和层次模型构建并实现了一种包含多元随机方差和非正态性的推理方法。在这种方法中，可以直接检查替代假设（如不同的误差分布）对结果推断的影响。此外，该项目开发了一个异常值诊断程序，用于随机方差的存在。本研究开发了一种分析时间序列数据的通用方法，例如股票价格，利率和其他金融序列，其中方差或波动性随时间变化。直到最近，这些数据的分析要么假设不变的方差，要么假设方差根据预先确定的模式变化。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通用的框架，而不依赖于现有方法的通常限制性假设。提供了一些统计工具来分析随机方差框架内的数据。本文提出了一种改进的分析时间序列数据的方法，并给出了几个基于金融时间序列的实例。

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.