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Papavasiliou, Anastasia and Ladroue, Christophe (2009) Parameter estimation for rough differential equations. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2009).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
We construct an estimator based on "signature matching" for differential equations driven by rough paths and we prove its consistency and asymptotic normality. Note that the the Moment Matching estimator is a special case of this estimator.
| Item Type: | Working or Discussion Paper (Working Paper) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Computer Science Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Parameter estimation, Differential equations |
| Series Name: | Working papers |
| Publisher: | University of Warwick. Centre for Research in Statistical Methodology |
| Place of Publication: | Coventry |
| Date: | 2009 |
| Volume: | Vol.2009 |
| Number: | No.1 |
| Number of Pages: | 15 |
| Status: | Not Peer Reviewed |
| Access rights to Published version: | Open Access |
| References: | [1] J. Li, P.G. Kevrekidis, C.W. Gear and I.G. Kevrekidis. Deciding the nature of the coarse equation through microscopic simulations: the baby-bathwater scheme. SIAM Rev. 49(3):469–487, 2007. [2] A. Papavasiliou, G.A. Pavliotis and A.M. Stuart. Maximum Likelihood Drift Estimation for Multiscale Diffusions. Stochastic Processes Applications (to appear). [3] T.J. Lyons, M.J. Caruna and T. L´evy. Differential Equations Driven by Rough Paths. In Ecole d’´et´e de Probabilit´es de Saint-Flour XXXIV (Editor: J. Picard), Springer, Berlin 2007. [4] P. E. Kloeden and E. Platen. Numerical Solution of Stochastic Differential Equations. Application of Mathematics 23. Springer-Verlag, Berlin 1999. [5] L. P. Hansen and J. A. Scheinkman. Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes. Econometrica 63(4):767- 804, 1995. [6] Y. A¨ıt-Sahalia and P. A. Mykland. An Analysis of Hansen-Scheinkman Moment Estimators for Discretely and Randomly Sampled Diffusions. Journal of Econometrics 144:1–26, 2008. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/35194 |
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