Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise

Erlin Guo; Cuixia Li; Patrick Ling; Fengqin Tang; Erlin Guo; Cuixia Li; Patrick Ling; Fengqin Tang

doi:10.3934/math.20231590

AIMS Mathematics

2023, Volume 8, Issue 12: 31070-31091. doi: 10.3934/math.20231590

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Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise

1.
School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China
2.
Department of Mathematics, Utah Valley University, Orem, USA
3.
School of Mathematics Sciences, Huaibei Normal University, Huaibei 235000, China

Received: 31 August 2023 Revised: 20 October 2023 Accepted: 12 November 2023 Published: 20 November 2023
MSC : 60G51, 62G35

High-frequency financial data are becoming increasingly available and need to be analyzed under the current circumstances for the market prices of stocks, currencies, risk analysis, portfolio management and other financial instruments. An emblematic challenge in econometrics is estimating the integrated volatility for financial prices, i.e., the quadratic variation of log prices. Following this point, in this paper, we study the estimation of integrated self-weighted volatility, i.e., the generalized style of integrated volatility, by using intraday high-frequency data with noise. In order to reduce the effect of noise, the "pre-averaging" technique is used. Both the law of large numbers and the central limit theorem of the estimator of integrated self-weighted volatility are established in this paper. Meanwhile, a studentized version is also given in order to make some statistical inferences. At the end of this article, the simulation results obtained to evaluate the accuracy of approximating the sampling distributions of the estimator are displayed.
- nonparametric estimation,
- self-weighted volatility,
- high-frequency data,
- microstructure noise,
- Itô process
Citation: Erlin Guo, Cuixia Li, Patrick Ling, Fengqin Tang. Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise[J]. AIMS Mathematics, 2023, 8(12): 31070-31091. doi: 10.3934/math.20231590

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Abstract

High-frequency financial data are becoming increasingly available and need to be analyzed under the current circumstances for the market prices of stocks, currencies, risk analysis, portfolio management and other financial instruments. An emblematic challenge in econometrics is estimating the integrated volatility for financial prices, i.e., the quadratic variation of log prices. Following this point, in this paper, we study the estimation of integrated self-weighted volatility, i.e., the generalized style of integrated volatility, by using intraday high-frequency data with noise. In order to reduce the effect of noise, the "pre-averaging" technique is used. Both the law of large numbers and the central limit theorem of the estimator of integrated self-weighted volatility are established in this paper. Meanwhile, a studentized version is also given in order to make some statistical inferences. At the end of this article, the simulation results obtained to evaluate the accuracy of approximating the sampling distributions of the estimator are displayed.

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