Contrast estimation of general locally stationary processes using coupling

TL;DR

This paper develops kernel-based estimators for time-varying parameters in local stationary processes, providing theoretical guarantees and demonstrating their effectiveness on various models and data sets.

Contribution

It extends existing results to infinite memory processes, establishing uniform consistency and asymptotic normality for a broad class of contrast-based estimators.

Findings

Estimators are consistent and asymptotically normal.

Effective for diverse models like ARMA, GARCH, and integer-valued processes.

Numerical experiments confirm estimator efficiency.

Abstract

This paper aims at providing statistical guarantees for a kernel based estimation of time varying parameters driving the dynamic of local stationary processes. We extend the results of Dahlhaus et al. (2018) considering the local stationary version of the infinite memory processes of Doukhan and Wintenberger (2008). The estimators are computed as localized M-estimators of any contrast satisfying appropriate contraction conditions. We prove the uniform consistency and pointwise asymptotic normality of such kernel based estimators. We apply our result to usual contrasts such as least-square, least absolute value, or quasi-maximum likelihood contrasts. Various local-stationary processes as ARMA, AR(infty), GARCH, ARCH(infty), ARMA-GARCH, LARCH(\infty),..., and integer valued processes are also considered. Numerical experiments demonstrate the efficiency of the estimators on both simulated and real data sets.