CAViaR Model Selection via Adaptive Lasso

The estimation and model selection of the 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, conventional automatic variable selection methods cannot be directly applied to this problem because the quantile lag components are latent. In this paper, we propose a two‐step approach to select the optimal CAViaR model. 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 regularity conditions, the proposed adaptive Lasso penalized quantile estimators enjoy the oracle properties. Finally, the proposed method is illustrated by a Monte Carlo simulation study and applied to analyzing the daily data of the S& P 500 return series.