Efficient robust nonparametric estimation in a semimartingale regression model

TL;DR

This paper introduces a robust, adaptive nonparametric estimation method for periodic functions in continuous-time regression models with dependent, non-Gaussian noise, applicable to financial market models with jumps.

Contribution

It develops a new model selection procedure based on weighted least squares for semimartingale noise, providing sharp non-asymptotic oracle inequalities and demonstrating robust efficiency.

Findings

Derived sharp non-asymptotic oracle inequalities.

Proved robustness and efficiency of the model selection procedure.

Applicable to financial models with jump processes.

Abstract

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a noise is non-gaussian Ornstein-Uhlenbeck process with the L\'evy process subordinator, which is used to model the financial Black-Scholes type markets with jumps. An adaptive model selection procedure, based on the weighted least square estimates, is proposed. Under general moment conditions on the noise distribution, sharp non-asymptotic oracle inequalities for the robust risks have been derived and the robust efficiency of the model selection procedure has been shown.