A robust nonparametric framework for reconstruction of stochastic differential equation models

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

doi:10.1016/j.physa.2016.01.016

Cited by 8 publications

(13 citation statements)

References 18 publications

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“…From now on, we shall refer to these methods as the KBR (Kernel Based Regression) and the POLY method (since it is based on orthonormal polynomials), respectively. We have included the POLY method since it is described as non-parametric in [15], although we find it closer to a parametric one (see Section I). We have also used these tests to further investigate the impact of the number of pseudo-inputs m on the estimates.…”

Section: Validation On Synthetic Datamentioning

confidence: 98%

“…Furthermore, we may only expect very accurate estimations for both f and g if the number of samples N is large. The time series' length used for SDE estimation depends on the study, but usual length requirements range from N ≈ 10 3 [15,17,24] to N ≈ 10 5 [13,25,26]. We would like to obtain estimates of f and g given a realization of the process x(t) without any assumption on their form (non-parametric regression).…”

Section: Gaussian Processes For Sde Estimationmentioning

confidence: 99%

“…To assess the validity of the SGP method, we compare its performance with the kernel based method [14] and with a version of the orthonormal polynomials method [15] using a set of simulated SDEs. From now on, we shall refer to these methods as the KBR (Kernel Based Regression) and the POLY method (since it is based on orthonormal polynomials), respectively.…”

Section: Validation On Synthetic Datamentioning

confidence: 99%

“…Recently, the use of orthogonal Legendre polynomials for approximating the functional form of the dynamical coefficients [15] was proposed. The weights of the polynomials are learnt by minimizing the squared regression error that results after discretizing the SDE with the Euler-Maruyama scheme.…”

Section: Introductionmentioning

confidence: 99%

“…In case of the simulated data, we compare our method with the kernel based regression [14] and the polynomial based method of [15]. In case of the real data, we apply our method to the study of financial data and climate transitions during the last glacial age.…”

Section: Introductionmentioning

confidence: 99%

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Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

et al. 2017

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The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a non-parametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudo-samples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behaviour of complex systems.

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Section: Validation On Synthetic Datamentioning

confidence: 98%

Section: Gaussian Processes For Sde Estimationmentioning

confidence: 99%

Section: Validation On Synthetic Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

et al. 2017

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Predicting the price of crude oil based on the stochastic dynamics learning from prior data

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Varying-Coefficient Stochastic Differential Equations with Applications in Ecology

Michelot

Glennie

Harris

et al. 2021

JABES

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Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomenon of interest, and their parameters often have a clear interpretation. These advantages come at the cost of requiring a relatively simple model specification. We propose a flexible model for SDEs with time-varying dynamics where the parameters of the process are nonparametric functions of covariates, similar to generalized additive models. Combining the SDE and nonparametric approaches allows for the SDE to capture more detailed, non-stationary, features of the data-generating process. We present a computationally efficient method of approximate inference, where the SDE parameters can vary according to fixed covariate effects, random effects, or basis-penalty smoothing splines. We demonstrate the versatility and utility of this approach with three applications in ecology, where there is often a modelling trade-off between interpretability and flexibility.Supplementary materials accompanying this paper appear online.

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A robust nonparametric framework for reconstruction of stochastic differential equation models

Cited by 8 publications

References 18 publications

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

Predicting the price of crude oil based on the stochastic dynamics learning from prior data

Varying-Coefficient Stochastic Differential Equations with Applications in Ecology

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