Likelihood ratio-type tests in weighted composite quantile regression of DTARCH models

The double-threshold autoregressive conditional heteroscedastic(DTARCH) model is a useful tool to measure and forecast the mean and volatility of an asset return in a financial time series. The DTARCH model can handle situations wherein the conditional mean and conditional variance specifications are piecewise linear based on previous information. In practical applications, it is important to check whether the model has a double threshold for the conditional mean and conditional heteroscedastic variance. In this study, we develop a likelihood ratio test based on the estimated residual error for the hypothesis testing of DTARCH models. We first investigate DTARCH models with restrictions on parameters and propose the unrestricted and restricted weighted composite quantile regression(WCQR) estimation for the model parameters. These estimators can be used to construct the likelihood ratio-type test statistic. We establish the asymptotic results of the WCQR estimators and asymptotic distribution of the proposed test statistics. The finite sample performance of the proposed WCQR estimation and the test statistic is shown to be acceptable and promising using simulation studies. We use two real datasets derived from the Shanghai and Shenzhen Composite Indexes to illustrate the methodology.

加权复合分位数回归方法在动态VaR风险度量中的应用

风险价值(VaR)因为简单直观,成为了当今国际上最主流的风险度量方法之一,而基于时间序列自回归(AR)模型来计算无条件风险度量值在实业界有广泛应用。本文基于分位数回归理论对AR模型提出了一个估计方法——加权复合分位数回归(WCQR)估计,该方法可以充分利用多个分位数信息提高参数估计的效率,并且对于不同的分位数回归赋予不同的权重,使得估计更加有效,文中给出了该估计的渐近正态性质。有限样本的数值模拟表明,当残差服从非正态分布时,WCQR估计的的统计性质接近于极大似然估计,而该估计是不需要知道残差分布的,因此,所提出的WCQR估计更加具有竞争力。此方法在预测资产收益的VaR动态风险时有较好的应用,我们将所提出的理论分析了我国九只封闭式基金,实证分析发现,结合WCQR方法求得的VaR风险与用非参数方法求得的VaR风险非常接近,而结合WCQR方法可以计算动态的VaR风险值和预测资产收益的VaR风险值。