April 24, 2014
Dr. Mohsen Pourahmadi
Professor Department of Statistics, Texas A&M University
Title: Thresholded Generalized Principal Component Regression: Forecasting with Many Predictors
Abstract:
Multiple time series, panel data and many other modern data matrices have dependence in their rows and columns, and the classical principal component analysis for low-rank approximation of such data matrices does not account for such two-way correlations. We develop a thresholded generalized principal component methodology to recover sparse and low-rank components of a data matrix by accounting for its two-way dependencies simulta-neously. For computing the components, we rely on orthogonal subspace iterations instead of the traditional power method and sparsity is attained by thresholding the components rather than solving penalized optimization problems. Our methodology is applicable to the multivariate regression and canonical correlation analysis for two-way dependent data, these connections enable us to improve prediction accuracy in regression with many predictors, and to facilitate interpretation of the components of the data matrix. We illustrate our methodology by forecasting the data in Stock and Watson (2012) consisting of quarterly data on 144 U.S. macroeconomic time series with 109 predictors, which is known to exhibit strong dependencies among the variables (columns) and temporal dependencies among observations (rows). The e ectiveness of the method is further demonstrated through simulations inspired by the superior performance of a predictor based on the rst ve principal components of the transformed macroeconomic time series data (Stock and Watson, 2012), and the age-old question of whether to forecast a (multiple) time series directly or after transforming to (near) stationarity. (Joint work with Ranye Sun).