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英文文献：Chasing volatility - A persistent multiplicative error model with jumps-追逐波动率-一个持续的乘性错误模型与跳跃
英文文献作者：Massimiliano Caporin,Eduardo Rossi,Paolo Santucci de Magistris
英文文献摘要：
The realized volatility of financial returns is characterized by persistence and occurrence of unpredictable large increments. To capture those features, we introduce the Multiplicative Error Model with jumps (MEM-J). When a jump component is included in the multiplicative specification, the conditional density of the realized measure is shown to be a countably infinite mixture of Gamma and K distributions. Strict stationarity conditions are derived. A Monte Carlo simulation experiment shows that maximum likelihood estimates of the model parameters are reliable even when jumps are rare events. We estimate alternative specifications of the model using a set of daily bipower measures for 7 stock indexes and 16 individual NYSE stocks. The estimates of the jump component confirm that the probability of jumps dramatically increases during the financial crises. Compared to other realized volatility models, the introduction of the jump component provides a sensible improvement in the fit, as well as for in-sample and out-of-sample volatility tail forecasts.
财务收益的已实现波动具有持续性和不可预测的大增量的特征。为了捕捉这些特征，我们引入了带跳跃的乘法误差模型(em - j)。当乘性规范中包含跳跃分量时，实现测度的条件密度被证明为伽玛分布和K分布的可数无限混合。导出了严格的平稳性条件。蒙特卡洛模拟实验表明，即使在跳跃是罕见事件的情况下，模型参数的极大似然估计也是可靠的。我们使用7个股票指数和16只纽约证券交易所股票的每日双动力指标来估计模型的替代规格。跳跃分量的估计证实了在金融危机期间跳跃的概率显著增加。与其他已实现的波动率模型相比，跳跃分量的引入在拟合以及样本内和样本外波动率尾部预测方面都有明显的改善。
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