Imperfection of the convergent cross-mapping method

In 2012, the Convergent Cross Mapping method for finding a causal relationship between system variables from their time series was published. This method is widely used in the study of systems of various nature - from assessing the effect of cosmic radiation on the climate, to the study of cerebral activity. The relevance and prospects of using this method prompted us to master it and to apply it to identifying causal relationships between the variables of the "biosphere-climate" system. The obtained results seemed suspicious and forced us to check carefully the adequacy of the CCM conclusions in relation to various model systems. This paper presents examples of model situations when the method gives false estimates of the presence of causal relationships and offers a possible explanation for the causes of false estimates appearance.