The tasks of forecasting time series arise in many areas of computer science. Algorithms based on machine learning do a good job of this task. In this work, we performed a comparative analysis of a number of algorithms for predicting time series by reservoir neural networks (echo-state networks) according to the forecast accuracy and the time it takes to build the forecast. To test forecasting algorithms, data sets obtained from the Mackey-Glass equation were used. The experiments showed that the sigmoidal and radial networks with a 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. The functionality of the mutual information of the input and output of the reservoir is maximized. 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 forecast accuracy.