Kalman Filtering Our group has developed a generalized Kalman filter based on quasi-Monte Carlo integration. Both the innovation and observation error can be arbitrary. The resulting procedure is efficient and accurate. We plan to use it in order to develop adaptive methods of the polysampling type, in which several distributional shapes for the innovation and/or observational errors are simultaneously entertained.
Dynamic Factor Analysis for Multivariate Time Series Models, where one or very few hidden time series are driving a set of observed time series are popular in financial theory and practice. If both the factor loadings and the factor itself are allowed to vary over time, such models become unidentifiable without further assumptions. Our group has developed such a model using a single common factor. We have shown how to compute estimates of the loadings or sensitivities for the observed variables and plan to develop strategies for model selection.