We consider large and moderate deviations for the empirical mean and covariance of hilbertian autoregressive processes. As an application we obtain moderate deviations principles for the eigenvalues and associated projectors of the empirical covariance.

The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This article aims at completing the theoretical study of the model...