On the Variance Estimators in Varying Coefficients Hilbertian Autoregressive Models

Accepted - April 2025

Abstract

The present paper is concerned with nonlinear autoregressive models in which the coefficients are assumed to be non constant but rather subject to random perturbations.  In the first order autoregressive process with random coefficients, we conduct a full fledged estimation theory for term variance of the correlation in order to distinguish  between an ordinary autoregressive model and a random coefficient one. Important  milestones are the almost sure convergence on the one hand and the rate of conver gence on the other hand. Furthermore, a simulation study is carried out to assess the  variance estimators’robustness.