A novel prediction method for sunshine and cloud cover is presented that minimizes the root mean square error of the predictions. It bases on a homogeneous recurrent Markov process with discrete states. The outstanding feature of the method is that the exact value of the prediction error is a priori known, prior to making any prediction. Within the limits of the underlying model to mimic the real world, it is an estimate for the best possible result of sunshine and cloud cover predictions. It is found that the best prediction alters from persistence over a short time horizon to the expectation of the steady state vector of the Markov process over a long prediction horizon, whereby the root mean square error changes from 0 to the standard deviation of the steady state vector. The prediction method was applied to two simple solar irradiance models under the assumption that the prediction errors are only caused by the stochastic behavior of sunshine and cloud cover. The calculated prediction errors were found to be in qualitative agreement with those reached in the real world. (C) 2014 Elsevier Ltd. All rights reserved.