Research Overview

My primary research focus lies in mathematical statistics, addressing the analysis of dependent data, particularly time series data, which is prevalent in numerous practical applications such as experiments, clinical studies, and financial markets. Many present-day time series datasets defy classical assumptions; they are often non-stationary, non-normally-distributed, high-dimensional, and massive in size.

A central theme of my work is developing flexible and statistically robust approaches to analyzing such complex data structures. Through rigorous mathematical theory, I design innovative statistical methods, using tools from empirical process theory, Stein’s method, and calculus, among others. My methods have offered novel insights, particularly in the domain of time series dynamics, which traditional methods fail to capture.

Completed Research

I have explored several key areas in the analysis of complex, dependent data:

1. Frequency Domain Analysis

  • Developed novel classes of periodograms by extending traditional autocovariance-based methods using joint distributions (copulas) and non-L2 loss functions.
  • Proved the consistency of estimators in frequency domain analysis.
  • Applications in financial markets have demonstrated the practicality of these methods.

2. Locally Stationary Time Series

  • Introduced new methods for the analysis of non-stationary time series data.
  • Developed model validation techniques that compare parametric and nonparametric approaches, leading to more robust analysis.

3. Change Detection

  • Created an improved method for detecting sudden structural changes in time series.
  • Developed a method for signals that are highly irregular after the change and used it to identify the onset of the COVID-19 pandemic.

4. Uncertainty Quantification

  • Broke new ground in uncertainty quantification by empoying Stein’s method to investigating the quality of the normal approximation for time series statistics.

For a more detailed look at my research and publications, please see my Publications page.

Current Research Interests

My future work includes expanding on the following:

1. Change Detection in High Dimensions

  • address high-dimensional change detection in regression models, where traditional methods fall short.

2. Irregularly Spaced Time Series Data

  • Developing methods to account for irregular observational intervals in time series.

3. Integrating Machine Learning with Time Series Analysis

  • Exploring how machine learning techniques can enhance the robustness and predictive power of time series models in large-scale datasets, especially in business analytics.

4. Uncertainty Quantification for Multiparameter Estimates

  • Improve uncertainty quantification in auto- and cross-covariance matrices through Stein’s method in multivariate settings.

Thank you for your interest in my research. If you have any questions or collaboration ideas, feel free to contact me.