Dr. Fan's research interest lies in the analysis of nonstationary and long-memory time series data that can be applied in many areas in finance, including financial markets prediction, financial systemic risk, portfolio investment, and risk management. Specifically, her research has been focused on developing statistical methods that can be used to deal with nonstationary issues when conducting statistical inference or making predictions. Her work in this context is directed towards:

1. Identification of informative economic and financial predictors of market returns. A new inference approach, MBB-IVXQR, is proposed in one of her recent papers to test for the significance of both nonstationary and stationary predictors. Different from the widely used filtration methods such as first-differencing, the IVX-filtration can maintain the maximum amount of information in a nonstationary data stream during the process of filtration. In the simulated experiments, it has been shown that the proposed method can effectively reduce more than 50% of the inference errors of the conventional methods.

2. Prediction of rare events in the financial markets. Her research also focuses on time series quantile regression and its application in finance. Quantile regression (QR) is a powerful statistical method that can be used to identify heterogeneous relationships between economic variables. In finance, it can be applied to identify useful information to predict the bad/good time in the market. With an understanding of the properties of the financial time series data, she has proposed several statistical methods to apply the quantile regression method to analyze the rare events in the financial markets.

3. Applying machine learning techniques to the analysis of high-dimensional, nonstationary time series data. Some of her recent work focuses on dealing with high-dimensional time series data when some time series are stationary, some are nonstationary, and some are cointegrated. Dr. Fan proposes to use the adaptive lasso method for selecting mixed-root predictors in an increasing-dimension framework, and prove its validity and efficiency. She also provides sufficient evidence from the analysis of financial markets to show that this method can greatly reduce the forecasting errors relative to conventional statistical methods.