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.
