On the Variance Estimators in Varying Coefficients Hilbertian Autoregressive Models: Accepted - April 2025

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.