Three essays on the econometric methods for high-dimensional economic and financial data using factor structures

This dissertation is a collection of three independent essays that explore novel econometric approaches for analyzing high-dimensional economic and financial data. A key commonality among these essays is the use of a factor structure, which aims to capture the underlying latent factors that drive the dynamics of the data. Moreover, each essay focuses on a unique aspect of the high-dimensional factor model, delving into diverse areas such as high-frequency data analysis, network analysis, and portfolio management in financial markets.

Chapter 1 studies high-frequency cross-sectional intraday stock returns which are contaminated with microstructure noise and exhibit co-movements. A dual factor model is introduced to capture the underlying dynamics of efficient prices and microstructure noise. Then a Double Principal Component Analysis (DPCA) method is proposed for the estimation of common factors for both efficient prices and microstructure noise.

Chapter 2 shifts the focus to network analysis for high-dimensional time series. Using a high-dimensional time-varying factor-adjusted vector autoregressive (VAR) model framework, two types of networks are investigated: a directed Granger causality network and an undirected partial correlation network. To estimate the transition and precision matrices, a penalized local linear method with a time-varying weighted group LASSO and a time-varying CLIME method is proposed.

Chapter 3 addresses the estimation of large dynamic precision matrices with multiple conditioning variables. To overcome the challenges of high dimensionality and cross-dependence, an approximate factor structure is introduced. A semiparametric method based on model averaging marginal regression is employed to approximate the underlying dynamic covariance matrices of the factors and the idiosyncratic components. The estimate of the dynamic precision matrices for the original time series is then obtained by utilising the Sherman-Morrison-Woodbury formula, and is applied in the construction of the minimum variance portfolio.

Throughout each chapter, asymptotic properties of the proposed estimates are established and validated through extensive Monte Carlo simulations. These methods are further applied to stock return datasets or a macroeconomic dataset to demonstrate their strong performance.