NSF Award
9761113
*** 9761113 Zhan 'I'his Small Business Innovation Research Phase I project will develop a flexible software environment for modeling time series which exhibit structural features such as level and trend breaks, as well as outliers. Such time series occur in many applications including finance, target tracking, and other kinds of recognition oriented signal processing. Currently, commercial software is not available that can adequately model such time series. The research will seek to estimate the parameters of such state space models using Markov chain Monte Carlo (MCMC) methods, which provide a feasible way of sampling from complex posterior distributions. MCMC has been recently applied to solve a variety of previously intractable problems involving high dimensional integration. In the time series context, MCMC methodology will be applied to (1) posterior densities for structural changes, including mixture distributions, (2) distributions involving hidden state processes for modeling switching behavior and detecting outliers, (3) thick tailed distributions of the state and the observation noise processes in order to robustly model anomalies and heterogeneity. Because of the wide variety of applications -- in environmental modeling, engineering, economics and statistics -- a ready market for this software is expected to develop. ***
