Estimation and Forecast Combination Under Robust T-Loss

• Activity Number: 295
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Gang Cheng*+
• Companies: University of Minnesota-Twin Cities
• Keywords: outliers ; forecast combination ; coefficient estimation ; linear regression

Abstract

Outliers commonly occurs in many areas such as economics, finance and other rich-data areas. However, the studies of forecast combination with frequent outliers are only a few in literature. In this work, we propose a loss function log(1 +x^2/v) (log-loss hereafter), which is the exponential kernel of a density function of t-distribution with degrees of freedom v and apply it on data with outliers in two directions: coefficient estimation and forecast combination. We show that t-loss with proper degrees of freedom provide more robust estimators. In addition, in forecast combination, we apply apply the t-loss in both the AFTER (Yang 2004) scheme and linear regression scheme. When there are heavy outliers, theoretical work shows 1). t-loss based AFTER works consistently better than the standard squared error based AFTER and many other popular combining methods; 2). t-loss based combined forecast from linear regression is not only more robust than that of square error loss but also better than all candidates in many situations. Numerical results support our theoretical work well.