Finding Methods and References for Stochastic Differential Equation Calibration

Summary

The document is a request for alternatives to maximum likelihood estimation and regression when calibrating parameters of a stochastic differential equation. The questioner reports practical difficulty maintaining an SDE calibrated through those approaches and wonders whether a derivative-free optimizer, such as downhill simplex, could be used to avoid additional mathematical complexity. No model, dataset, or calibration results are described, so the problem remains general.

The accepted response recommends consulting two R software projects and their associated papers as concise surveys of estimation and inference for stochastic processes. It suggests following the papers' citations and points readers toward sections on inference, but does not compare specific estimators, explain optimizer setup, or establish that simplex optimization addresses the stated maintainability concerns. The references are starting points for further study rather than a direct calibration recipe. Appropriate methods would depend on the SDE, observation frequency, noise assumptions, and computational requirements, none of which the document specifies.

Key ideas

• The question concerns alternatives to maximum likelihood and regression for estimating SDE parameters.
• The author is interested in derivative-free optimization because of calibration maintainability concerns.
• The response points to software packages and papers covering SDE estimation and stochastic-process inference.
• The document offers references rather than a method comparison or a step-by-step calibration procedure.

Tags

# Methods of SDE Calibration


# Methods of SDE Calibration












There is somewhere summary of methods that can be used to estimate parameters of SDE?

I currently using MLE and regression due to linear dependence between samples. I searching for something different due to many problems with maintainability of this SDE when using calibration method like this.

I think it should be exist some method that works similar to downhill-simplex algorithm, since I want avoid hassle with math, but I can't find any.

## Answer by Matt (score 4, accepted)

https://quant.stackexchange.com/a/22586

> There is somewhere summary of methods that can be used to estimate parameters of SDE?

If you'd like a brief survey, consider the following packages as well as the accompanying papers (note: you may want to follow the citations listed therein):

https://cran.r-project.org/web/packages/Sim.DiffProc/

- "Estimation of Stochastic Differential Equations with Sim.DiffProc Package": https://cran.r-project.org/web/packages/Sim.DiffProc/vignettes/FitSDE.pdf -- in particular, take note of the literature referenced in Section 1.

https://cran.r-project.org/web/packages/yuima/

- "The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations": http://www.jstatsoft.org/article/view/v057i04 -- in particular, take a look at Section 6, "Inference for stochastic processes."

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.