Groupwise Semiparametric Modeling: An LVME Approach

• Activity Number: 607
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Song Song*+ and Lixing Zhu
• Companies: University of Alabama and Hong Kong Baptist University
• Keywords: Time Series ; Covariance Estimation ; Regularization ; Sparsity ; Semiparametrics ; Variable Clustering

Abstract

The research described here is motivated by modeling a high dimensional time series dataset through groupwise information and sparse structure on explanatory variables. To arrive at a groupwise semiparametric modeling, for example for several key economic measures CPI, EMPl and FFR, a three-step-algorithm is suggested: first screening to reduce dimensionality, then clustering according to grouped explanatory variables and finally estimating coefficients with sign-constraints to produce meaningful economic interpretations. This algorithm is based on a large covariance matrix estimation (LVME) for the generalized $m$-dependent and $\beta$-mixing time series by hard thresholding regularization. For this purpose, the interplay between the estimator's convergence rate and the temporal dependence level is quantified and a cross-validation result is proved to justify the resampling scheme for threshold selection. This algorithm is evaluated in finite sample cases through a Monte Carlo experiment and applied to model economic and financial time series semiparametrically, which shows the superiorities over the linear modeling.