A robust nonparametric framework for reconstruction of stochastic differential equation models

Yalda Rajabzadeh, Amir Hossein Rezaie and Hamidreza Amindavar

Physica A: Statistical Mechanics and its Applications, 2016, vol. 450, issue C, 294-304

Abstract: In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler–Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

Keywords: Stochastic differential equation; Parameter estimation; Nonparametric method; Stationary process (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:450:y:2016:i:c:p:294-304

DOI: 10.1016/j.physa.2016.01.016

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