Estimation of time series by Maximum Mean Discrepancy

TL;DR

This paper introduces new minimum distance estimators for dependent time series data using approximated Maximum Mean Discrepancy, enabling robust parameter estimation even with complex models and latent variables.

Contribution

It develops a novel estimation method based on MMD for dependent data, including theoretical properties and simulation validation.

Findings

Estimators are robust to model misspecification.

Method performs well with latent variables.

Theoretical properties are established for dependent data.

Abstract

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When the latter one is intractable, it is approximated by simulation, allowing to accommodate most dynamic processes with latent variables. We derive the non-asymptotic and the large sample properties of our estimators in the context of absolutely regular/beta-mixing random elements. Our simulation experiments illustrate the robustness of our procedures to model misspecification, particularly in comparison with alternative standard estimation methods.