CAViaR Model Selection Via Adaptive Lasso

Zongwu Cai, Ying Fang and Dingshi Tian
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Zongwu Cai: Department of Economics, University of Kansa, Lawrence, KS 66045, USA
Ying Fang: The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China
Dingshi Tian: Department of Statistics, School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei 430073, China

No 202403, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: The estimation and model selection of conditional autoregressive value at risk (CAViaR) model may be computationally intensive and even impractical when the true order of the quantile autoregressive components or the dimension of the other regressors are high. On the other hand, automatic variable selection methods cannot be directly applied to this problem because the quantile lag components are latent. In this paper, we propose to identify the optimal CAViaR model using a two-step approach. The estimation procedure consists of an approximation of the conditional quantile in the first step, followed by an adaptive Lasso penalized quantile regression of the regressors as well as the estimated quantile lag components in the second step. We show that under some mild regularity conditions, the proposed adaptive Lasso penalized quantile estimators enjoy the oracle properties. Finally, the proposed method is illustrated by Monte Carlo simulation study and applied to analyzing the daily data of the S&P500 return series.

Keywords: CAViaR model; Adaptive Lasso; Model selection; Tail risk. (search for similar items in EconPapers)
JEL-codes: C32 C51 C58 (search for similar items in EconPapers)
Date: 2024-01, Revised 2024-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
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