Final prediction error and final interpolation error: A paradox? (Corresp.)

It is well-known in the theory of stationary stochastic process) that, given the true spectrum and subject to general conditions, the linear least squares predictor (i.e., extrapolator) has an error variance not smaller than the error variance of the linear least squares interpolator. It is then perhaps natural to expect that the same results would hold when the true spectrum is unknown, but can be estimated from data. In this correspondence the fallacy of this expectation is exposed by carefully analyzing a simple situation. The seemingly paradoxical phenomenon is further demonstrated by some simulation results. We conclude with a heuristic explanation.