In this study, a method of causality detection was designed to reveal coupling between dynamical systems represented by time series. The method is based on the predictions in reconstructed state spaces. The results of the proposed method were compared with outcomes of two other methods, the Granger VAR test of causality and the convergent cross-mapping. We used two types of test data. The first test example is a unidirectional connection of chaotic systems of Rössler and Lorenz type. The second one, the fishery model, is an example of two correlated observables without a causal relationship. The results showed that the proposed method of optimized mixed prediction was able to reveal the presence and the direction of coupling and distinguish causality from mere correlation as well.