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

Author

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  • Zhenjie Liang

    (School of Economics, Xiamen University, Xiamen 361005, China
    These authors contributed equally to this work.)

  • Futian Weng

    (School of Medicine, Xiamen University, Xiamen 361005, China
    National Institute for Data Science in Health and Medicine, Xiamen University, Xiamen 361005, China
    Data Mining Research Center, Xiamen University, Xiamen 361005, China
    These authors contributed equally to this work.)

  • Yuanting Ma

    (School of Economics and Management, East China Jiaotong University, Nanchang 330013, China)

  • Yan Xu

    (School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
    National Economic Engineering Laboratory, Dongbei University of Finance and Economics, Dalian 116025, China)

  • Miao Zhu

    (School of Statistics, Huaqiao University, Xiamen 361005, China)

  • Cai Yang

    (School of Business Administration, Hunan University, Changsha 410082, China)

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.

Suggested Citation

  • Zhenjie Liang & Futian Weng & Yuanting Ma & Yan Xu & Miao Zhu & Cai Yang, 2022. "Measurement and Analysis of High Frequency Assert Volatility Based on Functional Data Analysis," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1140-:d:785625
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    References listed on IDEAS

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    2. Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.

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