I am an Associate Professor at the Department of Mathematics, and an Affiliate Researcher at the Center for Applied Mathematics, and the Center for Artificial Intelligence and Robotics, at the University of Macau. Here is my Google Scholar page. 

I finished my Ph.D. in Statistics at the Hong Kong University of Science and Technology in 2010. During 2011-2012, I was an Assistant Professor in Economics at the Wang Yanan Institute for Studies in Economics and the Department of Statistics, at the Xiamen University. 

My current research interests are Statistics for Stochastic Processes, Financial Statistics, and Statistical Learning for Health Science. If you are interested in a Ph.D. in Statistics at the University of Macau, feel free to email me at liuzhi@um.edu.mo to discuss this.


  • 2006-2010: Ph.D, Statistics, Hong Kong University of Science & Technology. Advisor: Bingyi JING
  • 2003-2006: M.SC, Probability and Statistics, Lanzhou University
  • 1999-2003: B.SC, Computational Mathematics, Lanzhou University

Working Experience

  • 8/2018-Present   Associate Professor in Mathematics, University of Macau
  • 8/2012-7/2018   Assistant 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


  • Mathematics for Artificial Intelligence (PG course for CIS), Spring, 2024
  • Data Mining and Statistical Learning, Spring, 2022, 2023
  • Nonparametric Statistics, Fall, 2022, 2023
  • Linear Statistical Analysis, Spring, 2021, Fall, 2022
  • Advanced Statistics (PG course), Spring, 2022, 2024
  • Topics in Statistics and Data Science, Fall, 2021
  • Large Sample Theory (PG course), Fall, 2019-2020
  • Time Series Analysis, Spring, 2015–2020, Fall, 2023
  • Mathematical Modelling, Fall, 2013–2020
  • Stochastic Processes (PG course), Fall, 2014, 2018
  • Probability and Statistics, Spring, 2016, 2017
  • Statistical Methods in Engineering (Ph.D. course), Fall, 2014
  • Probability Theory, Fall, 2013
  • Engineering Mathematics, Spring, 2013
  • Calculus III, Fall, 2012

Ph.D. students supervised

  • JIANG Yu (2022–)
  • LIU Wenjing (2022–) Nonparametric estimation for the probability distances
  • TANG Jingwei (2021–)
  • BAI Lu (2019–) Hybrid approaches in machine learning prediction
  • ZHU Haibin (2020–2023): High-frequency inference on the price staleness. First Job: Tenure-track Assistant Professor, Jinan University (Guangzhou)
  • HE Lidan (2018–2021): Higher-order approximations and forecasts of volatility. First Job: Assistant professor, Nanjing University of Information Science & Technology
  • WAN Yi (2015–2019): Jackknife empirical likelihood-based Tests. First Job: Data Scientist, Huawei Technologies Co. Ltd.
  • LIU Qiang (2015–2018): Inference of spot volatilities under infinite variation jumps. First Job: Post-doctoral fellow, National University of Singapore (Now Tenure-track Assistant Professor, Shanghai University of Finance and Economics)
  • WANG Li (2014–2018): Realized Laplace transform of volatility with microstructure noise. First Job: Assistant professor, Macau University of Science and Technology.
  • LIU Yiqi (2014–2017, Co-supervisor): The effect of multiple records on volatility estimation via high-frequency financial data. First Job: Pingan FinTech. 

Master students supervised

  • XU Hantian, ZHOU Shunchao (2023–)
  • AN Ruofan, SUN Di (2022)
  • WONG Cho Him, DENG Wenlong, LI Rui, LIN Yang (2021–)
  • ZHUO Yihua (2020–)
  • LIU Wenjing (2020–2022)
  • ZHU Baowen (2019–2022)
  • YIN Shu (2018–2021)
  • DONG Jianqiao, FU Binchao (2018–2020)
  • LIU Peixi (2017–2020)
  • HUANG Yuling, SUN Jing (2017–2019)
  • U Cheok Meng, DENG Min (2015–2018)
  • WANG Jianqing, LIU Yiming, WAN Yi, LIU Ziqian (2013–2015)
  • SHE Zihang, ZHOU Biting (2012–2014)
  • DONG Hui (2012–2013)

Research Grants

  External Grants

  1. Statistical Learning of Chronic Kidney Disease in Macau (10/01/2022-09/01/2024), The Science and Technology Development Fund, Macau SAR, FDCT0041/2021/ITP, MOP $424,000. Sole PI.
  2. Statistical Inference of Distributions of Volatility with Applications (01/01/2020-31/12/2023), NSFC No.11971507, RMB 520,000. PI. (Co-PI: Jacky So, University of Macau)
  3. Studying the Non-synchronous Trading under Ultra-high Frequency (25/5/2018-24/5/2021), The Science and Technology Development Fund, Macau SAR, FDCT202/2017/A3, MOP $917,000. Sole PI.
  4. Efficient Estimation of Spot Volatility under General Jump Process (1/6/2017-31/5/2020), The Science and Technology Development Fund, Macau SAR, FDCT127/2016/A3, MOP $1,043,725. Sole PI.
  5. Efficient Estimation of Volatility Matrix under Presence of Infinite Variation Jumps with Applications (1/1/2015-31/12/2017), NSFC No.11401607, RMB 220,000. PI. (Co-PI: Jacky So, University of Macau), 
  6. FDCT Special Equipment Fund, The Science and Technology Development Fund, Macau SAR, FDCT043/2014/SA, MOP $204,120.
  7. Inference on Volatility Matrix of Big Data with Applications, (1/6/2014-31/5/2017), The Science and Technology Development Fund, Macau SAR, FDCT078/2013/A3, MOP $1,171,000. Sole PI.
  8. Statistical Inference of High-Frequency Data with Implementation (1/6/2013-31/12/2015), The Science and Technology Development Fund, Macau SAR, FDCT078/2012/A3, MOP$734,000. PI. (Co-PIs, XIONG Jie, DING Deng and SHU Lianjie, University of Macau). 

  Internal Grants

  1. Inference of price staleness with applications to high-frequency trading, (1/1/2023-31/12/2024), MYRG from University of Macau, MYRG2022-00118-FST, MOP$544,000. Sole PI.
  2. Statistical inference of spot correlation and spot market Beta under infinite variation jumps, (1/1/2022-31/12/2023), MYRG2020-00227-FST, MOP $600,000. Sole PI.
  3. 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.

  4. Inference on High-Frequency Data Some New Problems, (1/4/2015-31/3/2018), MYRG from University of Macau, MYRG2015-00184-FST, MOP $840,000. Sole PI.
  5. Inference on Volatility Matrix of Big Data with Applications, (24/6/2014-23/6/2017), Matching fund from University of Macau, MRG024/LZ/2014/FST, MOP $390,000. Sole PI.
  6. Studying Higher Order Moments of Daily Returns under High Frequency, (1/4/2014-31/3/2017), MYRG from University of Macau, MYRG2014-00001-FST, MOP $840,000. Sole PI.
  7. Statistical Inference of High-Frequency Data with Implementation, (1/8/2013-31/7/2015), Matching fund from University of Macau, MRG009/LZ/2013/FST, MOP $244,500. Sole PI.
  8. Statistical Inference of Semi-martingale with High-Frequency Data, (1/11/2012-31/10//2013), Startup fund from University of Macau, SRG023-FST12-LZ, MOP $100,000. Sole PI.

Selected Publications (Full Publications List)

  1. ZHU Haibin and LIU Zhi (2024). On Bivariate time-varying price staleness, Journal of Business and Economic Statistics42, 229-242.

  2. K. Ulrich Hounyo,  LIU Zhi and Rasmus T. Varneskov (2023). Bootstrapping Laplace transform of volatility, Quantitative Economics. 14, 1059-1103.
  3. FENG Xinwei, HE Lidan and LIU Zhi (2022). Large deviation principles of realized Laplace transform of volatility, Journal of Theoretical Probability. 35, 186–208.

  4. LIU Qiang and LIU Zhi (2022). Statistical Inference of spot correlation and spot market Beta under infinite variation jumps, Journal of Financial Econometrics, 20, 612-654.

  5. DING Li-zhong, LIU Zhi, LI Yu, LIAO Shi-zhong, LIU Yong, YANG Peng, YU Ge, SHAO Ling, GAO Xin (2019). Linear Kernel Tests via Empirical Likelihood for High-Dimensional Data,  AAAI2019. Acceptance rate: 16.2%

  6. WANG Li, LIU Zhi and XIA Xiao-chao (2019). Rate efficient estimation of realized Laplace transform of volatility with microstructure noise, Scandinavian Journal of Statistics. 46(3), 920-953.

  7. Yuta KOIKE and LIU Zhi (2019). Asymptotic properties of the realized skewness and related statistics, Annals of the Institute of Statistical Mathematics. 71(4), 703-741.

  8. KONG Xin-bing, LIU Zhi and ZHOU Wang (2019), A rank test for the number of factors with high-frequency data, Journal of Econometrics. 211(2), 439-460.

  9. LIU Yi-ming, LIU Zhi and ZHOU Wang (2019). A test for equality of two distributions via integrating characteristic functions, Statistica Sinica. 29, 1779-1801.

  10. HU Jiang, LI Wei-ming, LIU Zhi and ZHOU Wang (2019). High-dimensional covariance matrices in elliptical distributions with application to spherical test, Annals of Statistics. 47(1), 527-555.

  11. 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.

  12. CHENG Cong-hua, LIU Yi-ming, LIU Zhi and ZHOU Wang (2018). Balanced augmented Jackknife Empirical Likelihood for two-sample U-Statistics. SCIENCE CHINA Mathematics61, 1129-1138.

  13. LIU Qiang, LIU Yi-qi and LIU Zhi (2018). Estimating spot volatility in the presence of infinite variation jumps, Stochastic Processes and their Applications, 128, 1958-1987.

  14. KONG Xin-bing, LIU Zhi, ZHAO Peng and ZHOU Wang (2017). SURE estimates under dependence and heteroscedasticity, Journal of Multivariate Analysis, 161, 1-11.

  15. 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.

  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 the 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. LIU Zhi (2016). Estimating integrated co-volatility with partially miss-ordered high-frequency data. Statistical Inference for Stochastic Processes, 19(2), 175-197.

  21. 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.

  22. JING Bing-yi, LIU Zhi and KONG Xin-bing (2014). On the estimation of integrated volatility with jumps and microstructure noise. Journal of Business & 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

  23. 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.

  24. 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.

  25. 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.

  26. JING Bing-yi, KONG Xin-bing, LIU Zhi and Per MYKLAND (2012). On the jump activity index for semi-martingales. Journal of Econometrics, 166(2), 213-223.

  27. 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, 558-568.

  28. 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.


  1. 全國大學生數學建模競賽三十週年服務銀質紀念獎章, 2022
  2. Teaching Excellence Award, 2021, FST, University of Macau.
  3. 全國大學生數學建模競賽優秀指導教師, 2017(二十五週年), 2022(三十週年)
  4. Research Excellence Award, 2017, FST, University of Macau.
  5. Travel grant award for PIMs, Mathematical Science Research Institute, Berkeley, CA, USA, 2010

Contact Details

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

Room: E11-3072
Telephone: (853) 8822-4494
Fax: (853) 8822-2426
Email: liuzhi@um.edu.mo