On the robustness to small trends of parameter estimation for continuous-time stationary models with memory

TL;DR

This paper demonstrates that a smoothed periodogram method for estimating parameters in continuous-time stationary models remains highly robust even when a small trend contaminates the data, extending previous discrete-time results.

Contribution

It provides a continuous-time analogue to prior discrete-time robustness results, showing the effectiveness of smoothed periodogram in the presence of small trends.

Findings

Robustness of smoothed periodogram to small trends

Extension of discrete-time results to continuous-time models

Validation through theoretical analysis

Abstract

The paper deals with a question of robustness of inferences, carried out on a continuous-time stationary process contaminated by a small trend, to this departure from stationarity. We show that a smoothed periodogram approach to parameter estimation is highly robust to the presence of a small trend in the model. The obtained result is a continuous version of that of Hede and Dai (Journal of Time Series Analysis, 17, 141-150, 1996) for discrete time processes.