A number of algorithms for predicting time series by reservoir neural networks (echo-state networks) are considered. The algorithms comparative analysis by the accuracy of the forecast and the time of construction of the forecast is performed. The experiments showed that the sigmoidal and radial networks with a self-organization map (SOM-projector) give the most accurate forecast, but they are also the least fast. A new reservoir optimization algorithm is proposed: a direct version of the Infomax method. This algorithm requires non-negativity of data values, but it works much faster than the well-known iterative version of Infomax and a radial network with a SOM-projector, although it slightly reduces the accuracy of the forecast.