基于LAD-LASSO的多门限波动率模型估计与应用

Estimation and Application of Multi-Threshold Volatility Models Based on LAD-LASSO

本文研究一类具有多门限结构的条件异方差自回归模型(T-CHARM)的估计和应用。针对门限个数未知以及金融数据的厚尾性质,我们采用最小绝对偏差套索算法(LAD-LASSO)同时估计门限个数和模型的未知参数。该方法在模型误差项四阶矩不存在时仍然有效,放宽了经典LASSO方法在门限模型上的适用场合。蒙特卡洛模拟表明,在门限个数的正确识别率、门限值和波动率参数值的估计方面,LAD-LASSO方法均具有优良的有限样本表现。本文将提出的LAD-LASSO方法结合T-CHAR模型,应用于沪深300指数日度收益率数据的建模和预测。实证结果表明,与采用LAD方法估计的经典GARCH模型相比,本文提出的方法在样本内拟合和样本外预测方面均有优越表现。

We study the estimation and application of a class of Threshold-Conditional Heteroscedasticity Autoregressive Models(T-CHARM)with Multiple Thresholds.Considering the unknown number of thresholds and the heavy-tailed property of financial data,we use the Least Absolute Deviation Lasso(LAD-LASSO)algorithm to estimate the unknown parameters and the number of thresholds simultaneously.This method remains effective even when the fourth moment of the model error term does not exist,which relaxes the applicability of the classical LASSO method in threshold models.Monte Carlo simulations show that the LAD-LASSO method has excellent finite sample performance in terms of the correct identification rate of threshold numbers, estimation of threshold values, and volatility parametervalues. The proposed LAD-LASSO method with the T-CHARM is applied to model and forecast thedaily returns of the CSI 300 Index. Empirical results show that compared to the classical GARCH modelestimated by the LAD approach, the proposed method has superior performance in both in-sample fittingand out-of-sample forecasting.