Title1：Large dimensional empirical likelihood

Speaker：Prof.Wang Zhou （National University of Singapore）

Time：Fri, Sep.15, 2017, AM 09:30-10:30

Title2：Efficient estimation of spot volatility with presence of infinite variation jumps

Speaker：Prof. Zhi Liu  （University of Macau）

Time：Fri, Sep.15, 2017, AM 10:30-11:30

Location:Room 4318, Building No.4, Wushan Campus

Abstract1: In this talk, by adding two pseudo-observations to the original data set, I will talk about the asymptotic normality of the log empirical likelihood ratio statistic. In practice, I suggest to use the normalized F distribution to approximate the distribution of the log empirical likelihood ratio statistic. Simulation results show the excellent performance of this approximation.

Abstract2: We propose a kernel estimator for the spot volatility of a semi-martingale at a given time point by using high frequency data, where the underlying process accommodates a jump part of infinite variation. The estimator is based on the representation of the characteristic function of Levy processes. The consistency of the proposed estimator is established under some mild assumptions. By assuming that the jump part of the underlying process behaves like a symmetric stable Levy process around 0, we establish the asymptotic normality of the proposed estimator. In particular, with a specific kernel function, the estimator is variance efficient. We conduct Monte Carlo simulation studies to assess our theoretical results and compare our estimator with existing ones.