Statistical Methods in Finance 2025

Parametric Estimation of SDEs under Indirect Observability from Multiscale Data

By: Ilya Timofeyev
University of Houston, USA

In this talk we consider parametric estimation of diffusions under indirect observability from approximate data. Indirect observability refers to situations in which the data are generated by a dynamical model (or observations) that can be approximated by the estimated stochastic differential equations. In particular, we assume that the approximating process converges to the estimated process in a suitable sense. We demonstrate that under indirect observability, multiscale effects may lead to inconsistent estimation. To remedy this, we develop explicit criteria for asymptotic consistency in terms of the convergence rate, the sub-sampling time-step, the number of sampled points, etc. We illustrate our results using slow–fast multiscale systems, SDEs with a multiscale potential, and the estimation of the volatility equation in the Heston model.