Measurement and Analysis of High Frequency Assert Volatility Based on Functional Data Analysis

Abstract

Information and communication technology have enabled the collection of high-frequency financial asset time series data. However, the high spatial and temporal resolution nature of these data makes it challenging to compare financial asset characteristics patterns and identify the risk. To address this challenge, a method for realized volatility calculation based on the functional data analysis (FDA) method is proposed. A time–price functional curve is constructed by the functional data analysis method to calculate the realized volatility as the curvature integral of the time–price functional curve. This method could effectively eliminate the interference of market microstructure noise, which could not only allow capital asset price to be decomposed into a continuous term and a noise term by asymptotic convergence, but also could decouple the noise from the discrete-time series. Additionally, it could obtain the value of volatility at any given time, which is no concern about correlations between repeated, mixed frequencies and unequal intervals sampling problems and relaxes the structural constraints and distribution setting of data acquisition. To demonstrate our methods, we analyze a per-second level financial asset dataset. Additionally, sensitivity analysis on the selection of the no equally spaced sample is conducted, and we further add noise to ensure the robustness of our methods and discuss their implications in practice, especially being conducive to more micro analysis of the volatility of the financial market and understanding the rapidly changing changes.

Keywords

• functional data analysis
• high frequency data
• Bernstein basis function
• curvature