Estimation of spot volatility with superposed noisy data |
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| Affiliation: | 1. Department of Mathematics, University of Macau, Macau SAR, China;2. UMacau Zhuhai Research Institute, Zhuhai, China;1. School of Economics, Shandong University, China;2. School of Business & Law, Edith Cowan University, Australia;3. School of Finance, Shandong University of Finance and Economics, China;1. Department of Information and Finance Management at the National Taipei University of Technology, Taipei, Taiwan;2. Department of Business Management at the National Taipei University of Technology, Taipei, Taiwan;3. Discipline of Finance at College of Management at Yuan Ze University, Taoyuan, Taiwan |
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| Abstract: | By using high frequency financial data, we nonparametrically estimate the spot volatility at any given time point, while the simultaneous presence of multiple transactions and market microstructure noise in the observation procedure are considered. Our estimator is based on the summation of the locally ranged increments, while kernel smoothing give us spot volatility. Besides, the microstructure noise can be estimated and removed, if it is modeled as bid-ask spread, which is a frequently used assumption. The consistency and asymptotic normality of the estimator are established. We do some simulation studies to assess the finite sample performance of our estimator. The estimator is also applied to some real data sets, further, the relationship between multiple records and spot volatility is also explored. |
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| Keywords: | High frequency financial data Spot volatility Range-based estimation Kernel estimate Multiple records Microstructure noise Central limit theorem |
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