Associate Professor, University of Hong Kong

Jul 2022 - Current

Assistant Professor, University of Hong Kong

Jul 2016 - Jul 2022

Assistant/Associate Professor, Chinese Academy of Sciences

Jan 2011 - Jul 2016

Ph.D in Statistics, Hong Kong University of Science and Technology

2006 - 2010

B.Sc in Mathematics, University of Science and Technology of China

2002 - 2006

Fellow, International Statistical Institute

Since 2023

Fellow, Journal of Econometrics

Since 2023

My current research focuses on four topics:

Machine learning in finance

I am tackling several interesting problems in finance by combining the machine learning methods and the statistical learning methods. For example, with my co-authors, I have developed a new CQVAE method for asset pricing. This method combines the VAE method with the quantile factor model to learn the whole distribution of returns. Moreover, with my co-authors, I have developed a new graph-based conditional moments (GRACE) method to do big portfolio selection. The GRACE method combines the factor-augmented temporal graph convolutional network (FTGCN) with the quantiled conditional moments (QCM) method. Due to the supervised learning feature of the QCM method, the GRACE method can do portfolio selection based on thousands of stocks or more.

Time series quantile learning

I am proposing several new methods to learn time series quantiles. First, with my co-author, I have proposed a new QCM method to learn the conditional variance, skewness, and kurtosis. The QCM method is a supervised learning procedure, since it learns the conditional higher-moments via the conditional quantiles. Moreover, due to its regression nature, the QCM method not only allows the conditional quantiles to be mis-specified to some extent, but also enjoys the convenience in computation without any constraints in model parameters. Second, I have proposed a new generalized EWMA quantile method to study the non-stationary quantiles. The generalized EWMA quantile method can be used with a sound statistical inference procedure. Particularly, it provides us a data-driven method to select the weighting parameters. Meanwhile, I am working on several new non-stationary quantile methods by including the distributional information of the data to improve the efficiency.

Complex time series inference

I am providing several new inference methods to study complex time series. With my co-authors, I have proposed a new matrix GARCH model to study conditional heteroskedasticity; I have proposed a new test for independence under non-stationarity; I have proposed a new test to check the validity of instrumental variables, etc.

Panel data analysis

I am constructing several new methods to study panel data. With my co-authors, I have proposed a new family of spatial models to investigate the spatial effects in variance, and I also have proposed an inverse DID framework for policy evaluation. Meanwhile, I have several on-going projects to study the dynamic panel and spatio-temporal data.

In the past, I have proposed several methodologies for financial time series analysis, nonlinear time series analysis, non-stationary time series analysis, and goodness-of-fit testing.

[8] Su, B. and Zhu, K. (2024), Inference for the panel ARMA-GARCH model when both N and T are large. PDF Codes

[7] Song, K., Jiang, F. and Zhu, K. (2024), Estimation for conditional moment models based on martingale difference divergence. PDF Codes

[6] Yu, C., Li, D., Jiang, F. and Zhu, K. (2023), Matrix GARCH Model: Inference and Application. PDF

[5] Zhu, Z., Zhang, N. and Zhu, K. (2023), Big portfolio selection by graph-based conditional moments method. PDF Supplementary materials Codes

[4] Zhang, N. and Zhu, K. (2023), Quantiled conditional variance, skewness, and kurtosis by Cornish-Fisher expansion. PDF Codes

[3] Su, B. Zhu, F. and Zhu, K. (2023), Statistical inference for the logarithmic spatial heteroscedasticity model with exogenous variables. PDF

[2] Zhang, N., Yu, H. and Zhu, K. (2023), How effective is the regional joint environmental policy in China? Evidence from inverse difference-in-differences. PDF News report from China Environment News (In Chinese)

[1] Zhu, K. (2020), Hausman tests for the error distribution in conditionally heteroskedastic models. PDF

[36] Yang, X., Zhu, Z., Li, D. and Zhu, K. (2024), Asset pricing via the conditional quantile variational autoencoder. Journal of Business & Economic Statistics 42, 681-694. PDF Journal Link Codes

[35] Zhu, K. (2023), A new generalized exponentially weighted moving average quantile model and its statistical inference. Journal of Econometrics 237, 105510. PDF Journal Link Supplement+Codes

[34] Cheung, Y.Y.H., Lam, K.F., Zhang, H., Kwan, C.W., Wat, K.P., Zhang, Z., Zhu, K., Cheung, Y.K. and Yin, G. (2023), A randomized controlled experiment for comparing face-to-face and online teaching during COVID-19 pandemic. Frontiers in Education, 8. PDF Journal Link

[33] Jiang, F., Li, D., Li, W.K. and Zhu, K. (2023), Testing and modelling for the structural change in covariance matrix time series with multiplicative form. Statistica Sinica 33, 787-818. PDF Journal Link

[32] Luo, D., Zhu, K., Gong, H. and Li, D. (2023), Testing error distribution by kernelized Stein discrepancy in multivariate time series models. Journal of Business & Economic Statistics 41, 111-125. PDF Journal Link Codes

[31] Gong, H. and Zhu, K. (2022), Info intervention and its causal calculus. In 1st Conference on Causal Learning and Reasoning, California, United States. PDF Journal Link

[30] Ling, S. and Zhu, K. (2022), Self-weighted LSE and residual-based QMLE of ARMA-GARCH models. Journal of Risk and Financial Management 15, 90. PDF Journal Link

[29] Wang, G., Zhu, K. and Shao, X. (2022), Testing for the martingale difference hypothesis in multivariate time series models. Journal of Business & Economic Statistics 40, 980-994. PDF Journal Link

[28] Liu, M., Zhu, F. and Zhu, K. (2022), Multifrequency-band tests for white noise under heteroskedasticity. Journal of Business & Economic Statistics 40, 799-814. PDF Journal Link

[27] Liu, M., Zhu, F. and Zhu, K. (2022), Modeling normalcy-dominant ordinal time series: An application to air quality level. Journal of Time Series Analysis 43, 460-478. PDF Journal Link

[26] Zhou, J., Jiang, F., Zhu, K. and Li, W.K. (2022), Time series models for realized covariance matrices based on the matrix-F distribution. Statistica Sinica 32, 755-786. PDF Journal Link

[25] Wang, G., Zhu, K., Li, G. and Li, W.K. (2022), Hybrid quantile estimation for asymmetric power GARCH models. Journal of Econometrics 227, 264-284. PDF Journal Link

[24] Jiang, F., Li, D. and Zhu, K. (2021), Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model. Journal of Econometrics 224, 306-329. PDF Journal Link

[23] Wang, G., Li, W.K. and Zhu, K. (2021), New HSIC-based tests for independence between two stationary multivariate time series. Statistica Sinica 31, 269-300. PDF Journal Link

[22] Wang, Q. and Zhu, K. (2020), On a measure of lack of fit in nonlinear cointegrating regression with endogeneity. Statistica Sinica 30, 371-396. PDF Journal Link

[21] Jiang, F., Li, D. and Zhu, K. (2020), Non-standard inference for augmented double autoregressive models with null volatility coefficients. Journal of Econometrics 215, 165-183. PDF Journal Link

[20] Li, D. and Zhu, K. (2020), Inference for asymmetric exponentially weighted moving average models. Journal of Time Series Analysis 41, 154-162. PDF Journal Link

[19] Zhu, K. (2019), Statistical inference for autoregressive models under heteroscedasticity of unknown form. Annals of Statistics 47, 3185-3215. PDF Journal Link

[18] Li, D., Guo, S. and Zhu, K. (2019), Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity. Econometric Reviews 38, 319-331. PDF Journal Link

[17] Wang, Q., Wu, D. and Zhu, K. (2018), Model checks for nonlinear cointegrating regression. Journal of Econometrics 207, 261-284. PDF Journal Link

[16] Li, D., Zhang, X., Zhu, K. and Ling, S. (2018), The ZD-GARCH model: A new way to study heteroscedasticity. Journal of Econometrics 202, 1-17. PDF Journal Link

[15] Zhu, K., Li, W.K. and Yu, P.L.H. (2017), Buffered autoregressive models with conditional heteroscedasticity: An application to exchange rates. Journal of Business & Economic Statistics 35, 528-542. PDF Journal Link

[14] Zhu, K. (2016), Bootstrapping the portmanteau tests in weak auto-regressive moving average models. Journal of the Royal Statistical Society, Series B 78, 463-485. PDF Journal Link Codes

[13] Zhu, K. and Li, W.K. (2015), A new Pearson-type QMLE for conditionally heteroskedastic models. Journal of Business & Economic Statistics 33, 552-565. PDF Journal Link

[12] Chen, M. and Zhu, K. (2015), Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations. Journal of Econometrics 189, 313-320. PDF Journal Link

[11] Zhu, K. and Ling, S. (2015), LADE-based inference for ARMA models with unspecified and heavy-tailed heteroscedastic noises. Journal of the American Statistical Association 110, 784-794. PDF Journal Link

[10] Zhu, K. and Ling, S. (2015), Model-based pricing for financial derivatives. Journal of Econometrics 187, 447-457. PDF Journal Link

[9] Zhu, K. and Li, W.K. (2015), A bootstrapped spectral test for adequacy in weak ARMA models. Journal of Econometrics 187, 113-130. PDF Journal Link

[8] Zhu, K., Yu, P.L.H. and Li, W.K. (2014), Testing for the buffered autoregressive processes. Statistica Sinica 24, 971-984. PDF Journal Link

[7] Guo, S., Ling, S. and Zhu, K. (2014), Factor double autoregressive models with application to simultaneous causality testing. Journal of Statistical Planning and Inference 148, 82-94. PDF Journal Link

[6] Ling, S., Zhu, K. and Chong, C.Y. (2013), Diagnostic checking for non-stationary ARMA models with an application to financial data. North American Journal of Economics and Finance 26, 624-639. PDF Journal Link

[5] Zhu, K. (2013), A mixed portmanteau test for ARMA-GARCH model by the quasi-maximum exponential likelihood estimation approach. Journal of Time Series Analysis 34, 230-237. PDF Journal Link

[4] Zhu, K. and Ling, S. (2013), Quasi-maximum exponential likelihood estimators for a double AR(p) model. Statistica Sinica 23, 251-270. PDF Journal Link

[3] Zhu, K. and Ling, S. (2012), The Global weighted LAD estimators for finite/infinite variance ARMA(p, q) models. Econometric Theory 28, 1065-1086. PDF Journal Link

[2] Zhu, K. and Ling, S. (2012), Likelihood ratio tests for the structural change of an AR(p) model to a threshold AR(p) model. Journal of Time Series Analysis 33, 223-232. PDF Journal Link

[1] Zhu, K. and Ling, S. (2011), Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models. Annals of Statistics 39, 2131-2163. PDF Journal Link