Sufficient Dimension Reduction Methodology in Forecasting

Economists and policy makers have more data at their disposal than ever before. Extracting the most relevant information prevents reacting to idiosyncratic movements and can lead to more precise forecasts and macro/microeconomic analyses. However, how to use these data effectively is an open problem. Dynamic Factor Models are pervasive in macro-econometrics and financial econometrics for both measuring co-movement and forecasting time series. However, the data reduction in DFMs comprises of summarizing the information in large data sets with a few components that capture a large proportion of their total variability without considering the forecasting ability of the reduced data. Sufficient Dimension Reduction (SDR) is a collection of tools for reducing the dimension of multivariate data in regression problems without losing inferential information for modeling the response. SDR uses many noisy signals in the observable data to extract information about the underlying structural sources of comovement that can be used to inform the building of forecasting models. This project will extend existing and develop new SDR methodology in econometric modeling and forecasting. SDR methods and data analysis tools will be developed to identify and estimate exhaustive reductions, including nonlinear data reductions, which have been marginally investigated in the DFM context. Furthermore, SDR methods for (a) targeted PCA and (b) for large p-small T (many predictors, few observations) time series regressions based on Krylov subspaces will be developed. Envelope models for multivariate response forecasting, such as central banks` macro forecasts, will be also developed and applied. The proposed research intends to make a significant contribution to the development of statistical tools that reduce data complexity in order to understand and model the underlying relationships and structures that drive the economy and obtain more accurate forecasts.

The research supported in this project developed tools for the effective utilization of large datasets in many areas of human activity and, in particular, in Economics and Finance. The research contributed novel statistical methodology with new techniques for the analysis of high-dimensional data in the field of Econometrics, as well as in practically all other fields that produce large amounts of data. Statistical tools that reduce data complexity in order to understand and model the underlying relationships and structures in the data were developed. Sufficient reductions of a large dataset, where all relevant information is condensed and simplified and all irrelevant is discarded, are computed. An important and scientifically interesting, yet surprising, result, is that a single combination of macro-economic variables is underlying the workings of the economy. Another important result of this project was that it led to new formulations of dependence for complex multidimensional data structures. Two doctoral theses and many publications in first tier journals were supported by this project.