A Perturbation Method to Optimize the Parameters of Autoregressive Conditional Heteroscedasticity Model

  • Xuejie FengEmail author
  • Chiping Zhang


As a linear regression parameter estimation method, the least square method plays an indispensable role in the parameter estimation of ARCH model. Although the least squares solution can minimize the sum of the squared errors, it will cause uneven distribution of errors, that is, some fitting errors are too large, and some fitting errors are too small, which will lead to overfitting. In response to this situation, we adopt a novel perturbation method to solve this problem. The specific theoretical derivation of the perturbation method is given in this paper. It takes parameters estimated by the least squares method as its initial iteration value. The maximum fitting error will decrease continuously from a series of iterations to final convergence. Furthermore, based on the perturbation method, this paper finds a condition that makes the ARCH model satisfy the non-negative limit of parameters. The experimental process uses real stock fund’s fluctuation data for fitting analysis and prediction. The experimental results show that the perturbation method can achieve the expected effect in the parameter estimation of the ARCH model, it can also effectively ensure that the fitting errors fluctuate within the controllable range when predicting the price fluctuation of stock funds in the future.


Perturbation Maximum error minimization Prediction Heteroscedasticity 

Mathematics Subject Classification

40A05 47N10 97M40 90C30 


Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and Animal Rights

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors.

Informed Consent

Informed consent was obtained from all individual participants included in the study.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.School of International BusinessQingdao Huanghai UniversityQingdaoChina

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