Explicit Bivariate Rate Functions for Large Deviations in AR(1) and MA(1) Processes with Gaussian Innovations

Abstract

We investigate large deviations properties for centered stationary AR(1) and MA(1) processes with independent Gaussian innovations, by giving the explicit bivariate rate functions for the sequence of random vectors (SnIn the AR(1) case, we also give the explicit rate function for the bivariate random sequence (Wn)) n 2 , as well. In the AR(1) case, we present a new proof for an already known result on the explicit deviation function for the Yule-Walker estimator.