Factorisable sparse tail event curves

Shih-Kang Chao, Wolfgang Härdle and Ming Yuan

No 2015-034, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: In this paper, we propose a multivariate quantile regression method which enables localized analysis on conditional quantiles and global comovement analysis on conditional ranges for high-dimensional data. The proposed method, hereafter referred to as FActorisable Sparse Tail Event Curves, or FASTEC for short, exploits the potential factor structure of multivariate conditional quantiles through nuclear norm regularization and is particularly suitable for dealing with extreme quantiles. We study both theoretical properties and computational aspects of the estimating procedure for FASTEC. In particular, we derive nonasymptotic oracle bounds for the estimation error, and develope an efficient proximal gradient algorithm for the non-smooth optimization problem incurred in our estimating procedure. Merits of the proposed methodology are further demonstrated through applications to Conditional Autoregressive Value-at-Risk (CAViaR) (Engle and Manganelli; 2004), and a Chinese temperature dataset.

Keywords: high-dimensional data analysis; multivariate quantile regression; quantile regression; value-at-risk; nuclear norm; multi-task learning (search for similar items in EconPapers)
JEL-codes: C38 C55 C63 G17 G20 (search for similar items in EconPapers)
Date: 2015
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