Multivariate time series is an active area of research in many academic disciplines such as Economics, Environmental Science, Finance, and Statistics among others. Since many observed series are not low dimensional, traditional methods lead to models with poor performance because too many parameters are estimated. Statistical methods in this proposal deal with these issues. Procedures proposed here bypass the generalized eigenvalue problems associated with traditional methods for dimensionality reduction which create serious difficulties in the theory and practice of data analysis. Simultaneous parsimonious modeling of signal and noise is addressed. An entirely new method based on exponential prediction is outlined in this proposal.
There is substantial interest among researchers in building parsimonious models and in developing effective methods for prediction. This proposal has been motivated in part by a need to analyze air pollution and macroeconomic data. In the study of air pollution, it is important to model multivariate time series consisting of pollutants, particulates and meteorological variables, and their impact on cardiovascular and respiratory mortality. Information obtained from such analyses has implications for policy on public health. The results of this research will be used to analyze air pollution and macroeconomic data. More generally, this proposal addresses issues in analysis of high dimensional time series that have wide applications. The educational aspect of this proposal includes monitoring and teaching graduate students the theory and practice of multivariate time series.
