On the realized joint Laplace transform of volatilities with application to test the volatility dependence
研究了利用高频数据重叠增量估计两个半鞅波动率的联合拉普拉斯变换，提出更有效的估计量，并构建了波动率依赖性的检验方法。
In this paper, we investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0,T] by using overlapped increments of high-frequency data. The proposed estimator is robust to the presence of finite variation jumps in price processes. The related functional central limit theorem for the proposed estimator has been established. Compared with the estimator with non-overlapped increments, the estimator with overlapped increments improves the asymptotic estimation efficiency. Furthermore, we study the asymptotic theory of estimator under the long time span setting and employ it to create a feasible test for the dependence between volatilities. Finally, simulation and empirical studies demonstrate the performance of proposed estimators.