Essays on high-frequency financial econometric - LI, Qiyuan (Institutional Knowledge at Singapore Management University, 2024)
This dissertation consists of three papers contributing to the theory of estimation and inference of high-frequency financial data. In the second chapter, a general framework is introduced for optimal nonparametric spot volatility estimation based on intraday range data, comprised of the first, highest, lowest, and last prices over a given time interval. Employing a decisiontheoretic approach together with a coupling-type argument, the form of the nonparametric estimator is directly tailored to the specific volatility measure of interest and the relevant loss function. The resulting new optimal estimators offer substantial efficiency gains compared to existing commonly used range-based procedures. The third chapter extends the previous chapter to handle multiple candlesticks, proposing a computationally more efficient algorithm for spot volatility estimation. Additionally, an exact simulation scheme is introduced to address biases in Euler discretization, enabling precise risk comparison and further analysis involving extreme values of Brownian motions. The fourth chapter addresses the uniform inference problem for high-frequency data that includes prices, volumes, and trading flows. Such data is modeled within a general state-space framework, where the latent state process is corresponding risk indicators, e.g., volatility, price jump, average order size, and arrival of events. The functional estimators are formed as a collection of localized estimates across different time points. Although the proposed estimators do not admit a functional central limit theorem, a Gaussian strong approximation, or coupling, is established under in-fill asymptotics to facilitate feasible inference. The proposed methodology is applied to distinguish the informative part from the Federal Open Market Committee speeches, and to analyze the impact of social media activities on cryptocurrency markets.