英文标题：
《A note on the Nelson Cao inequality constraints in the GJR-GARCH model:
  Is there a leverage effect?》
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作者：
Stavros Stavroyiannis
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最新提交年份：
2017
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英文摘要：
  The majority of stylized facts of financial time series and several Value-at-Risk measures are modeled via univariate or multivariate GARCH processes. It is not rare that advanced GARCH models fail to converge for computational reasons, and a usual parsimonious approach is the GJR-GARCH model. There is a disagreement in the literature and the specialized econometric software, on which constraints should be used for the parameters, introducing indirectly the distinction between asymmetry and leverage. We show that the approach used by various software packages is not consistent with the Nelson-Cao inequality constraints. Implementing Monte Carlo simulations, despite of the results being empirically correct, the estimated parameters are not theoretically coherent with the Nelson-Cao constraints for ensuring positivity of conditional variances. On the other hand ruling out the leverage hypothesis, the asymmetry term in the GJR model can take negative values when typical constraints like the condition for the existence of the second and fourth moments, are imposed.
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中文摘要：
金融时间序列的大多数程式化事实和一些风险价值度量是通过单变量或多变量GARCH过程建模的。由于计算原因，高级GARCH模型无法收敛的情况并不罕见，通常的节约方法是GJR-GARCH模型。文献和专门的计量经济学软件中存在分歧，应将约束条件用于参数，间接引入不对称和杠杆之间的区别。我们表明，各种软件包使用的方法与Nelson-Cao不等式约束不一致。实施蒙特卡罗模拟，尽管结果在经验上是正确的，但估计参数在理论上与Nelson Cao约束不一致，无法确保条件方差的正性。另一方面，排除杠杆假设，当施加二阶矩和四阶矩等典型约束条件时，GJR模型中的不对称项可以取负值。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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