For wave energy converter control applications, autoregressive (AR) models have been proposed as a simple wave forecasting method, solely based on measured or estimated values of the past wave elevation (or excitation force) signal. Using offline-filtered wave time series, AR models can achieve accurate forecasts several wave periods into the future. In this paper, the AR method is examined from the broader perspective of linear, Gaussian processes. In particular, assuming Gaussian waves and perfect knowledge of the wave spectrum, it is possible to derive a theoretically-optimal wave elevation predictor. It is shown that, in realistic situations, AR models can achieve a performance comparable to the theoretically optimal, spectrum-based predictor, both in simulated wave time series and using actual wave elevation records.