Functional Data Analysis and Extensions for Financial Data

It’s worth noting that functional data analysis greatly enriches existing data analysis methods. It brings a broader perspective to investigate data structures. Thus, this thesis focuses on the field of functional data analysis and its extension methods. We begin by revisiting the fundamental methodologies of functional data analysis that support the overall concept of this thesis. After this explanatory stage, this thesis contributes three main parts. Part one concentrates on the application of the functional data analysis techniques based on the functional high-frequency intra-day volatility dataset. Part two is intended for realising the real-time short-term dynamic updating forecasts. Specifically, we apply the univariate time series forecasting method and the multivariate time series forecasting method to obtain the principal component scores forecasting. Also, to forecast the dynamic updating, we adopt five models and compare their results in light of the accuracy of measuring. The contribution of this part lies in the incorporation of the rolling window methods into the sequence of functional time series forecasting techniques. And the remaining parts consist in developing the novel functional curve clustering algorithm, which includes proximity measurement and time-shift clustering.

After conducting the numerical simulation experiments, we find the proposed model has an outstanding performance with respect to functional data clustering. Also, identifying the proximity threshold is a central issue in the proposed algorithm. Then, the proximity measurement algorithm is used on a newly gathered COVID-19 functional dataset, a topic of high concern. Meanwhile, we apply the time-shift clustering algorithm to another freshly collected NASDAQ Composite functional dataset. And both two models deliver remarkable outcomes in terms of identifying trajectories of functional curves and accomplishing further clustering. Finally, through this thesis, the effectiveness of the functional data analysis techniques in the application is demonstrated, and the superiority of the functional expansion methods is verified.