  We consider the problem of estimating the autocorrelation operator of an
autoregressive Hilbertian process. By means of a Tikhonov approach, we
establish a general result that yields the convergence rate of the estimated
autocorrelation operator as a function of the rate of convergence of the
estimated lag zero and lag one autocovariance operators. The result is general
in that it can accommodate any consistent estimators of the lagged
autocovariances. Consequently it can be applied to processes under any mode of
observation: complete, discrete, sparse, and/or with measurement errors. An
appealing feature is that the result does not require delicate spectral decay
assumptions on the autocovariances but instead rests on natural source
conditions. The result is illustrated by application to important special
cases.
