Abstract
Existing estimators for the jump activity index only made use of the price dynamics of assets. In this study, we incorporate trading information and propose a trading-ow-adjusted (TA) estimator for the jump activity index for pure-jump Itô semimartingales observed at high frequencies. We derive the central limit theorem of the estimator and perform simulation studies that justify the theory. The new estimator is shown to be more efficient in terms of the convergence rate as compared with the existing estimators, which use only the price information under some realistic conditions. Empirical analysis shows estimates with lower standard errors than those that do not incorporate the trading information.
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Acknowledgments
The first author was supported by National Natural Science Foundation of China (Grant Nos. 11201080 and 11571250) and Priority Academic Program Development of Jiangsu Higher Education Institu- tions. The second author was supported by National Natural Science Foundation of China (Grant No. 11501503), Qinglan Project of Jiangsu Province, National Science Foundation of Jiangsu Province of China (Grant No. BK20181417) and Jiangsu Province College Science Key Foundation (Grant No. 17KJA110001). The third author was supported by National Natural Science Foundation of China (Grant No. 71874028), State Key Pro- gramme of National Natural Science Foundation of China (Grant No. 71331006) and the Fundamental Research Funds for the Central Universities in University of International Business and Economics (Grant No. 16YQ05). The authors thank the two anonymous reviewers for their extensive and constructive suggestions, which helped improve this paper significantly.
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Kong, X., Liu, G. & Xie, S. Trading-flow assisted estimation of the jump activity index. Sci. China Math. 63, 2363–2378 (2020). https://doi.org/10.1007/s11425-018-9442-1
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DOI: https://doi.org/10.1007/s11425-018-9442-1