Linear regression estimation using intraday high frequency data

Wenhui Feng; Xingfa Zhang; Yanshan Chen; Zefang Song; Wenhui Feng; Xingfa Zhang; Yanshan Chen; Zefang Song

doi:10.3934/math.2023662

AIMS Mathematics

2023, Volume 8, Issue 6: 13123-13133. doi: 10.3934/math.2023662

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Linear regression estimation using intraday high frequency data

School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China

Received: 18 February 2023 Revised: 16 March 2023 Accepted: 19 March 2023 Published: 03 April 2023
MSC : 62J05, 62M10

Intraday high frequency data have shown important values in econometric modeling and have been extensively studied. Following this point, in this paper, we study the linear regression model for variables which have intraday high frequency data. In order to overcome the nonstationarity of the intraday data, intraday sequences are aggregated to the daily series by weighted mean. A lower bound for the trace of the asymptotic variance of model estimator is given, and a data-driven method for choosing the weight is also proposed, with the aim to obtain a smaller sum of asymptotic variance for parameter estimators. The simulation results show that the estimation accuracy of the regression coefficient can be significantly improved by using the intraday high frequency data. Empirical studies show that introducing intraday high frequency data to estimate CAPM can have a better model fitting effect.
- linear regression,
- intraday high frequency data,
- quadratic programming
Citation: Wenhui Feng, Xingfa Zhang, Yanshan Chen, Zefang Song. Linear regression estimation using intraday high frequency data[J]. AIMS Mathematics, 2023, 8(6): 13123-13133. doi: 10.3934/math.2023662

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Abstract

Intraday high frequency data have shown important values in econometric modeling and have been extensively studied. Following this point, in this paper, we study the linear regression model for variables which have intraday high frequency data. In order to overcome the nonstationarity of the intraday data, intraday sequences are aggregated to the daily series by weighted mean. A lower bound for the trace of the asymptotic variance of model estimator is given, and a data-driven method for choosing the weight is also proposed, with the aim to obtain a smaller sum of asymptotic variance for parameter estimators. The simulation results show that the estimation accuracy of the regression coefficient can be significantly improved by using the intraday high frequency data. Empirical studies show that introducing intraday high frequency data to estimate CAPM can have a better model fitting effect.

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