Zhi LIU  劉志
Associate Professor

Academic Qualifications | Working experience | Teaching | Research | Publications | Services | Awards | Contact Details

Academic Qualifications
Working experience

8/2018-Present Associate Professor in Mathematics, University of Macau
8/2012-7/2018Assistant Professor in Mathematics, University of Macau
9/2011-7/2012 Assistant Professor in Economics, Xiamen University
1/2011-8/2011 Research Associate, Hong Kong University of Science & Technology


Courses taught in recent 5 years

Ph.D students supervised

Master students supervised


Research Interests

Research Grants

External Grants

  1. Studying the non-synchronous trading under ultra-high frequency (1/6/2018-31/5/2021), Macau Government, FDCT 202/2017/A3, MOP $917,000. Sole PI.
  2. Efficient Estimation of Spot Volatility under General Jump Process (01/06/2017-31/05/2020), Macau Government, FDCT127/2016/A3, MOP $1,043,725. Sole PI.
  3. Efficient Estimation of Volatility Matrix under Presence of Infinite Variation Jumps with Applications (01/01/2015-31/12/2017), NSFC No.11401607, RMB 220,000. PI. (Co-PI: Jacky So, University of Macau)
  4. FDCT Special Equipment Fund, Macau Government, FDCT043/2014/SA, MOP $204,120.
  5. Inference on Volatility Matrix of Big Data with Applications, (01/06/2014-31/05/2017), Macau Government, FDCT078/2013/A3, MOP $1,171,000. Sole PI.
  6. Statistical Inference of High Frequency Data with Implementation (01/08/2013-31/12/2015), Macau Government, FDCT078/2012/A3, MOP $734,000. PI. (Co-PIs, Xiong Jie, Ding Deng and Shu Lianjie, University of Macau)

Internal Grants

  1. Joint Laplace Transform of Volatility Matrix, (1/1/2019-31/12/2021), MYRG from University of Macau, MYRG2018-00107-FST, MOP $588,000. Sole PI.
  2. Inference on High Frequency Data: Some New Problems, (01/04/2015-31/03/2018), MYRG from University of Macau, MYRG2015-00184-FST, MOP $840,000. Sole PI.
  3. Studying Higher Order Moments of Daily Returns under High Frequency, (01/04/2014-31/03/2017), MYRG from University of Macau, MYRG2014-00001-FST, MOP $840,000. Sole PI.
  4. Statistical Inference of Semi-martingale with High Frequency Data, (01/11/2012-31/10/2013), Startup fund from University of Macau, SRG023-FST12-LZ, MOP $100,000. Sole PI.

Conference Grants

  1. Annual Meeting of Asian Finance Association (25/06/2016–28/06/2016), CGFST008-2016-LZ, MOP$10,520.
  2. World Finance Conference (02/07/2014–04/07/2014), CG023-FST2014-LZ, MOP$20,400.
  3. World Finance & Banking Symposium (16/12/2013–17/12/2013), CG197-FST2013-LZ, MOP$11,850.
  4. Asian Finance Association Annual Meeting (15/07/2013–17/07/2013), CG121-FST2013-LZ, MOP $11,300.


Refereed journal articles

  1. WANG Li, LIU Zhi and XIA Xiao-chao (2018). Realized Laplace Transform of Volatility with Microstructure Noise, Scandinavian Journal of Statistics. Accepted.
  2. WAN Yi, LIU Zhi and DENG Min (2018). Empirical-likelihood-based test for equality of two distributions using distance of characteristic functions, Statistics. Accepted.
  3. WANG Li, LIU Zhi and XIA Xiaochao (2018). Realized Laplace Transforms for Pure Jump Semi-martingales with Presence of Microstructure Noise, Soft Computing. To appear.
  4. HU Jiang, LI Weiming, LIU Zhi and ZHOU Wang (2018). High-dimensional covariance matrices in elliptical distributions with application to spherical test. To appear in Annals of Statistics.
  5. Yuta KOIKE and LIU Zhi (2018). Asymptotic properties of the realized skewness and related statistics. To appear in Annals of the Institute of Statistical Mathematics.
  6. LIU Yi-ming, LIU Zhi and ZHOU Wang (2018). A test for equality of two distributions via integrating characteristic functions. To appear in Statistica Sinica.
  7. LIU Zhi, XIA Xiaochao, ZHOU Guoliang (2018). Pre-averaging estimate of high dimensional integrated covariance matrix with noisy and asynchronous high-frequency data. Random Matrices: Theory and Applications. 1850005.
  8. LIU Zhi, KONG Xin-bing and JING Bing-yi (2018). Estimating the integrated volatility using high frequency data with zero durations, Journal of Econometrics. 204, 18-32
  9. LIU Qiang, LIU Yiqi and LIU Zhi and WANG Li (2018). Estimation of spot volatility with superposed noisy data, North American Journal of Economics and Finance. 44, 62-79.
  10. LIU Qiang, LIU Yiqi and LIU Zhi (2017). Efficient estimation of spot volatility with presence of infinite variation jumps. To appear in Stochastic Processes and their Applications.
  11. KONG Xin-bing, LIU Zhi, ZHAO Peng and ZHOU Wang (2017). SURE estimates under dependence and heteroscedasticity, Journal of Multivariate Analysis, 161, 1-11.
  12. Cheng Cong-hua, Liu Yi-ming, Liu Zhi and Zhou Wang (2017). Balanced Augmented Jackknife Empirical Likelihood for Two Sample U-Statistics. SCIENCE CHINA Mathematics, forthcoming. DOI: 10.1007/s11425-016-9071-y.
  13. Liu Yi-qi, Liu Qiang, Liu Zhi and Ding Deng (2017). Determining the integrated volatility via limit order books with multiple records. Quantitative Finance, 17(11), 1697-1714.
  14. Li Zhou-ping, Liu Yi-ming and Liu Zhi (2017). Empirical Likelihood and General Relative Error Criterion with Divergent Dimension. Statistics, 51(5), 1006-1022.
  15. Lai Peng, Song Feng-li, Chen Kai-wen and Liu Zhi (2017). Model free feature screening with dependent variable in ultrahigh dimensional binary classification. Statistics & Probability Letters, 125, 141-148.
  16. Cai Zong-wu, Jing Bing-yi, Kong Xin-bing and Liu Zhi (2017). Nonparametric regression with nearly integrated regressors under long run dependence. Econometrics Journal, 20(1), 118-138.
  17. Kong Xin-bing, Liu Zhi, Yao Yuan and Zhou Wang (2017). Sure Screening by Ranking the Canonical Correlations. Test, 26(1), 46-70.
  18. Liu Zhi (2017). Jump-robust Estimation of Volatility with Simultaneous Presence of Microstructure Noise and Multiple Observations. Finance and Stochastics, 21(2), 427-469.
  19. Jing Bing-yi, Liu Zhi and Kong Xin-bing (2017). Estimating the volatility functionals with multiple transactions. Econometric Theory, 33(2), 331-365.
  20. Lai Peng, Liu Yi-ming, Liu Zhi and Wan Yi (2017). Model free feature screening for ultrahigh dimensional models with responses missing at random. Computational Statistics & Data Analysis, 105, 201-216.
  21. Cheng Cong-hua, Liu Yi-ming and Liu Zhi (2017). Empirical likelihood ratio under infinite second moment. Communication in Statistics-Theory and Methods, 46(14), 6909-6915.
  22. Cheng Cong-hua, Liu Zhi and Wan Yi (2017). Empirical likelihood for compound Poisson processes under infinite second moment. Communication in Statistics-Theory and Methods, 46(17), 8618-8627.
  23. Li Wei-ming and Liu Zhi (2016). A test for the complete independence of high-dimensional random vectors. Journal of Statistical Computation and Simulation, 86(16), 3135-3140.
  24. Xia Xiao-chao, Liu Zhi and Yang Hu (2016). Regularized estimation for the least absolute relative error models with a diverging number of covariates. Computational Statistics & Data Analysis, 96, 104-119.
  25. Liu Zhi (2016). Estimating integrated co-volatility with partially miss-ordered high frequency data. Statistical Inference for Stochastic Processes, 19(2), 175-197.
  26. Liu Zhi, Xia Xiao-chao and Zhou Wang (2015). A test for equality of two distributions via jackknife empirical likelihood and characteristic functions. Computational Statistics & Data Analysis, 92, 97-114.
  27. Yin Ju-liang, Ding Deng, Liu Zhi and Suiyang Khoo (2015). Some properties of finite-time stable stochastic nonlinear systems. Applied Mathematics and Computation, 259, 686-697.
  28. Kong Xin-bing, Liu Zhi and Jing Bing-yi (2015). Testing for pure-jump processes for high-frequency data. Annals of Statistics, 43(2), 847-877.
  29. Li Cui-xia, Chen Jin-yuan, Liu Zhi and Jing Bing-yi (2014). On integrated volatility of Itô semimartingales when sampling times are endogenous (2014). Communication in Statistics-Theory and Methods, 43, 5263-5275.
  30. Jing Bing-yi, Liu Zhi and Kong Xin-bing (2014). On the estimation of integrated volatility with jumps and microstructure noise. Journal of Business and Economic Statistics, 32(3), 457-467. The article was the JBES Invited Address presented at the Joint Statistical Meetings, Boston, Massachusetts, August 2-7, 2014
  31. Jing Bing-yi, Kong Xin-bing, Liu Zhi and Zhang Bo (2014). Evaluating the hedging error in price processes with jumps present. Statistics and Its Interface, 6(4), 413-425.
  32. Jing Bing-yi, Li Cui-xia and Liu Zhi (2013). On Estimating the Integrated Co-Volatility Using Noisy High-Frequency Data with Jumps. Communication in Statistics-Theory and Methods, 42(21), 3889-3901.
  33. Wang Kent, Liu Jun-wei and Liu Zhi (2013). Disentangling the Effect of Jumps on Systematic Risk with a New Estimator of Integrated Co-Volatility. Journal of Banking and Finance, 37, 1777-1786.
  34. Abbas Ahmed, Kong Xin-bing, Liu Zhi, Jing Bing-yi and Gao Xin (2013). Automatic peak selection by a Benjamini-Hochberg-based algorithm. PLoS ONE, 8(1): e53112. doi: 10.1371/journal.pone.0053112.
  35. Liu Zhi, Abbas Ahmed, Jing Bing-yi and Gao Xin (2012). WaVPeak: picking NMR peaks through wavelet transform and volume-based filtering. Bioinformatics, 28(7), 914-920.
  36. Jing Bing-yi, Kong Xin-bing and Liu Zhi (2012). Modeling high frequency financial data by pure jump processes. Annals of Statistics, 40(2) 759-784.
  37. Jing Bing-yi, Kong Xin-bing, Liu Zhi and Per Mykland (2012). On the jump activity index for semimartingales. Journal of Econometrics, 166(2) 213-223.
  38. Jing Bing-yi, Kong Xin-bing and Liu Zhi (2011). Estimating the jump activity index under noisy observations using high frequency data. Journal of American Statistical Association, 106(494), 558-568.
  39. Jing Bing-yi, Liu Zhi and Kong Xin-bing (2010). Testing for diffusion in a discretely observed semi-martingale. Journal of the Korean Statistical Society, 39 (3), 357-370.
  40. Jing Bing-yi, Kong Xin-bing, Liu Zhi and Zhang Bo (2009). Stochastic regression and its application to hedging in finance. SCIENCE CHINA Mathematics, 52(6), 1365-1372

Refereed conference proceedings

  1. Liu Zhi, Wang Kent and Liu Jun-wei (2013). Realized skewness at high frequency and link to conditional market premium, Proceedings 59th ISI World Statistics Congress, 3982-3987.

Book Chapter

  1. LIU Zhi, Zhong Hua-chao (2013). On estimating co-volatility with non-synchronous high frequency data. Statistical Review, 7, 67-77. Beijing Economic Science Press. In Chinese.


University and Faculty service

  1. Member of Master Students Recruitment Committee (2012-present)
  2. Member of PhD students Recruitment Committee (2014-2015, 2017-)
  3. Member of Department Self-Review Report Drafting Committee (2014-2015)
  4. Chair of Mathematical Modeling Advisory Committee (2015-present)
  5. Affiliate of East Asia College (2015-present)
  6. Supervisor committee of final year project of Honours College (2015, 2016)
  7. Supervisor of final year project of Department of Mathematics (2016)
  8. Member of New Staff Committee (2012)
  9. Member of University Staff Basket Ball Team (2013-2014)
  10. Member of organization committee of the 2015 UM Workshop on Probability and Statistics (2015)

External service

Professional Societies
  1. Member of Asian Finance Association
  2. Member of Institute of Mathematical Statistics
  3. Member of The Econometric Society
  4. Reviewer of Mathematical Review
Anonymous referee for the Journals
  1. Annals of Statistics, Journal of the American Statistical Association, Journal of Econometrics, Journal of Business and Economic Statistics, Scandinavian Journal of Statistics, Econometric Theory, Journal of Time Series Analysis, Electrical Journal of Probability, Electrical Journal of Statistics, Science in China, Communication in Statistics–Theory and Method, Communication in Statistics–Simulation and Computation, Emerging Markets Finance and Trade, Applied Mathematics–a Journal of Chinese Universities, Economics Research International, The North American Journal of Economics and Finance, Soft Computing, Accounting and Finance.

Invited talks and presentations

Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3072
Telephone: (853) 8822-4494
Fax: (853) 8822-2426
Email: liuzhi