Zhou Zhou - Research

My current research interest, in general, involves statistical inference of data with complex structures. The analysis of such data inevitably involves certain non- or semi-parametric statistical procedures since parametric specification of the complex data generating mechanism is difficult, if not impossible. A particular complex data structure is temporally ordered data, or time series data. Non-stationarity, high-dimensionality, and nonlinearity are widely recognized as the three major challenges for time series analysis in the big data era. These complicated data structures arise ubiquitously when a large number of stochastic processes are simultaneously recorded over a relatively long period of time. Oftentimes the complexity of the data prevents/discoverages researchers and practitioners from using the classical time series approaches, such as the stationary ARMA theory and methodology summarized in Box et al.'s well-known monograph.

Non-stationary Time Series Analysis

Non-stationarity refers to the temporal instability of the underlying data generating mechanism of a system of interest. In the big data era, non-stationarity is the rule rather than the exception for many temporally ordered systems. There are abundant challenges in the modeling, estimation, inference and prediction of such stochastic processes. Some of my works in this direction:

Zhou, Z. and Weibiao Wu (2009). Local Linear Quantile Estimation for Non-stationary Time Series. The Annals of Statistics, 37 2696-2729. Link
Zhou, Z. (2010). Nonparametric Inference of Quantile Curves for Non-stationary Time Series. The Annals of Statistics, 38 2187-2217. Link
Zhou, Z. (2013). Heteroscedasticity and Autocorrelation Robust Structural Change Detection. Journal of the American Statistical Association, 108 726-740. Link
Zhou, Z. (2014). Inference of Weighted V-statistics for Non-stationary Time Series and Its Applications.The Annals of Statistics, 42 87-114. Link
Zhou, Z. (2015). Inference for Non-stationary Time Series Regression with/without Inequality Constraints. Journal of the Royal Statistical Society, series B, 77 349-371.Link
Weichi Wu and Zhou, Z. (2018). Gradient-based Structural Change Detection for Non-stationary Time Series M-estimation. The Annals of Statistics, 46 1197-1224. Link
Xiucai Ding and Zhou, Z. (2023+). Auto-Regressive Approximations to Non-stationary Time Series, with Inference and Applications. The Annals of Statistics, to appear. ArXiv
Weichi Wu and Zhou, Z. (2023+). Multiscale Jump Point Detection under Complex Temporal Dynamics. ArXiv

High Dimensional Time Series Analysis

High dimensional time series are frequently encountered in, for example, economic, financial, medical and engineering applications. My current work in this direction mainly involves exploratory as well as structured (e.g. sparse, low rank) estimation and inference of high dimensional temporal systems. A few papers:

Xiucai Ding and Zhou, Z. (2020). Estimation and Inference for Precision Matrices of Non-stationary Time Series. The Annals of Statistics, 48 2455-2477. Link
Zhou, Z. and Holger Dette (2023+). Statistical Inference for High-Dimensional Panel Functional Time Series. Journal of the Royal Statistical Society, series B, to appear. ArXiv
Weichi Wu, Zhou, Z. (2023+). Adaptive Estimation for Evolutionary High-Dimensional Factor Models, And a Test for Static Factor Loadings. ArXiv
Yan Cui and Zhou, Z. (2023+). Simultaneous Inference for Time Series Functional Linear Regression. ArXiv
Tao Ma, Zhou, Z. and Constantinos Antoniou (2019). Dynamic Factor Model for Network Traffic State Forecast. Transportation Research, Part B, Methodological, 118 281-317. Link

Nonlinear Time Series Analysis

Nonlinear time series models have been proven to better explain the dynamics as well as provide more accurate estimations/forecasts for many temporal systems. My current work in this direction mainly involves 1) exploring and visualizing nonlinear dependence and 2) statistical inference of nonparametric nonlinear time series models. Some papers:

Zhou, Z. (2012). Measuring Nonlinear Dependence in Time Series, A Distance Correlation Approach. Journal of Time Series Analysis. 33 438-457. Link
Yan Cui, Jun Yang and Zhou, Z. (2023+). State-domain Change Point Detection for Nonlinear Time Series. Journal of Econometrics, to appear. Link
Xiucai Ding and Zhou, Z. (2023+). Simultaneous Sieve Inference for Time-Inhomogeneous Nonlinear Time Series Regression. ArXiv
Tao Ma, Zhou, Z. and Abdulhai, B. (2015). Nonlinear Multivariate Time-Space Threshold Vector Error Correction Model for Short Term Traffic State Prediction. Transportation Research, Part B, Methodological, 46 26-47. Link

Time-Frequency Analysis

Broadly speaking, time-frequency (TF) analysis is a branch of signal processing aiming to analyze signal from both time and frequency perspectives simultaneously. In recent years, linear, bilinear and nonlinear TF analysis tools have had an enormous impact on many applications, including and not limited to physiological, clinical, electromagnetic, acoustic and financial signal processing. It is clear that the subjects and the goals of TF analysis and non-stationary time series analysis are highly overlapped. Unfortunately, it seems that the non-stationary spectral domain theory and methodology in the time series literature have been developed largely independently from TF analysis. Over the last few years I have been working on several problems that bridge TF analysis and non-stationary time series analysis. Some papers:

Jun Yang and Zhou, Z. (2022). Spectral Inference under Complex Temporal Dynamics. Journal of the American Statistical Association, 117 133-155. Link
Matt Sourisseau, Hautieng Wu and Zhou, Z. (2022). Asymptotic Analysis of Synchrosqueezing Transform – toward Statistical Inference of Nonlinear-Type Time-Frequency Analysis. The Annals of Statistics, 50 2694-2712. Link
Hau-Tieng Wu and Zhou, Z. (2023+). Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation. Journal of the American Statistical Association, to appear. ArXiv

Sieve Nonparametric Estimation and Inference

The method of sieves (e.g. orthogonal basis expansions, splines, and artificial neural networks) refers to approximating an infinite dimensional space with a sequence of finer and finer finite dimensional subspaces. The advantages of the sieve method include that, among others, 1) the estimation accuracy and computational complexity of many sieve methods can be easily made adaptive to the smoothness of the functions of interest and 2) many sieve methods enjoy superior boundary behavior compared to local counterparts such as the kernel regression. Currently, I am working on some research projects toward nonparametric statistical estimation and inference via the method of sieves. Another current line of research involves exploring the intrinsic connections between the method of sieves and other nonparametric statistical methods. Some papers:

Xiucai Ding and Zhou, Z. (2020). Estimation and Inference for Precision Matrices of Non-stationary Time Series. The Annals of Statistics, 48 2455-2477. Link
Yan Cui and Zhou, Z. (2023+). Simultaneous Inference for Time Series Functional Linear Regression. ArXiv