Efficient drift parameter estimation for ergodic solutions of backward SDEs

TL;DR

This paper develops consistent and asymptotically normal quasi-maximum likelihood estimators for drift parameters in ergodic backward SDEs, handling unobserved stochastic integrals and semi-parametric models, with validation through simulations.

Contribution

It introduces novel estimation techniques for ergodic backward SDEs with unobserved components, extending existing methods to semi-parametric and non-Markovian settings.

Findings

Estimators are consistent and asymptotically normal.

Simulation studies show good convergence properties.

Method applies to a broad class of ergodic diffusions and backward SDEs.

Abstract

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our analysis is that the stochastic integral part is unobserved and non-parametric. Additionally, the drift may depend on the (unknown and unobserved) stochastic integrand. Our results hold for ergodic semi-parametric diffusions and backward SDEs. Simulation studies confirm that the methods proposed yield good convergence results.