Multihypothesis motion-compensating predictors combine several motion-compensated signals to predict the current frame of a video signal. This paper applies the wide-sense stationary theory of multihypothesis motion compensation for hybrid video codecs to multihypothesis motion estimation. This allows us to study the influence of the displacement error correlation on the efficiency of multihypothesis motion compensation. Reducing the displacement error correlation between the hypotheses decreases the variance of the multihypothesis prediction error. We derive a property for the displacement error correlation coefficient for an optimal multihypothesis motion estimator in the mean squared error sense. We observe for the wide-sense stationary model that jointly optimal motion estimation improves the prediction performance and reduces the prediction error variance up to 12 dB per accuracy refinement step compared to 6 dB per accuracy refinement step for uncorrelated displacement errors. Consequently, the gain of multihypothesis motion-compensated prediction with jointly optimal motion estimation over motion-compensated prediction increases by improving the accuracy of each hypothesis. We also discuss the combination of hypotheses with additive noise and extend the predictor by the optimum Wiener filter.