Iguchi, Yuga;
Beskos, Alexandros;
Graham, Matthew M;
(2022)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions.
arXiv: Ithaca, NY, USA.
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Abstract
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for the approximation of the intractable transition dynamics of the Stochastic Differential Equation (SDE) model over finite time periods. The scheme is applied for a step-size that is either user-selected or determined by the data. Recent research has highlighted the critical ef-fect of the choice of numerical scheme on the behaviour of derived parameter estimates in the setting of hypo-elliptic SDEs. In brief, in our work, first, we develop two weak second order sampling schemes (to cover both hypo-elliptic and elliptic SDEs) and produce a small time expansion for the density of the schemes to form a proxy for the true intractable SDE transition density. Then, we establish a collection of analytic results for likelihood-based parameter estimates obtained via the formed proxies, thus providing a theoretical framework that showcases advantages from the use of the developed methodology for SDE calibration. We present numerical results from carrying out classical or Bayesian inference, for both elliptic and hypo-elliptic SDEs.
Type: | Working / discussion paper |
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Title: | Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.48550/arXiv.2211.16384 |
Publisher version: | https://doi.org/10.48550/arXiv.2211.16384 |
Language: | English |
Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | CLT; data augmentation; hypo-elliptic diffusion; small time density expansion; stochastic differential equation |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
URI: | https://discovery.ucl.ac.uk/id/eprint/10186272 |
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