Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise
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 integr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231590?viewType=HTML |
| _version_ | 1797405551397699584 |
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| author | Erlin Guo Cuixia Li Patrick Ling Fengqin Tang |
| author_facet | Erlin Guo Cuixia Li Patrick Ling Fengqin Tang |
| author_sort | Erlin Guo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T03:11:38Z |
| format | Article |
| id | doaj.art-17604198c3a54b9786942e36c1468c95 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-09T03:11:38Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-17604198c3a54b9786942e36c1468c952023-12-04T01:30:49ZengAIMS PressAIMS Mathematics2473-69882023-11-01812310703109110.3934/math.20231590Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noiseErlin Guo0Cuixia Li 1Patrick Ling2Fengqin Tang31. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China1. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China2. Department of Mathematics, Utah Valley University, Orem, USA3. School of Mathematics Sciences, Huaibei Normal University, Huaibei 235000, ChinaHigh-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.https://www.aimspress.com/article/doi/10.3934/math.20231590?viewType=HTMLnonparametric estimationself-weighted volatilityhigh-frequency datamicrostructure noiseitô process |
| spellingShingle | Erlin Guo Cuixia Li Patrick Ling Fengqin Tang Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise AIMS Mathematics nonparametric estimation self-weighted volatility high-frequency data microstructure noise itô process |
| title | Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise |
| title_full | Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise |
| title_fullStr | Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise |
| title_full_unstemmed | Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise |
| title_short | Convergence rate for integrated self-weighted volatility by using intraday high-frequency data with noise |
| title_sort | convergence rate for integrated self weighted volatility by using intraday high frequency data with noise |
| topic | nonparametric estimation self-weighted volatility high-frequency data microstructure noise itô process |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231590?viewType=HTML |
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