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

数学科学：具有随机方差的时间序列非线性推理的统计方法

• 批准号: 9505109
• 负责人: Nicholas Polson
• 金额: $ 5万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505109&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Methods; Nonlinear

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.

提案：DMS 9505109 PI：Nick Polson机构：芝加哥大学标题：随机方差时间序列非线性推断的统计方法 摘要： 本计画发展并应用阶层式统计模式于非线性推论问题，以处理具有随机变异与非常态误差的多元资料的新领域。Jacquier，Polson和Rossi（1994）的先前研究表明，这种方法是 比通常的统计方法更好，如广义的方法， 矩，对于正态单变量随机方差的情况。本研究利用马尔可夫链蒙特卡罗技术和分层建模，构建和实现了一种推理方法，其中包括多变量随机方差和非正态性。在这种方法中，可以直接检查替代假设的影响，例如不同的误差分布对所得推论的影响。此外，该项目开发了一个离群值诊断程序，用于存在随机方差。 本研究发展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， 或者波动性，会随着时间而改变直到最近，这样的数据进行了分析，假设恒定的方差或方差变化根据预定的模式。 最近的统计工作表明，分析这些数据的更好方法是 假设方差随机变化。这种方法被称为随机方差 (or时间序列建模。这项研究提供了一个更一般的框架来分析这些模型，它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， 在随机方差框架内分析数据。本研究所提出的方法，提供了一种分析时间序列资料的改良方法，并以金融时间序列为例，进行了实证分析。