AbstractUnder the perfect prognosis approach, statistical downscaling methods learn the relationships between large‐scale variables from reanalysis and local observational records. These relationships are subsequently applied to downscale future global climate model (GCM) simulations in order to obtain projections for the local region and variables of interest. However, the capability of such methods to produce future climate change signals consistent with those from the GCM, often referred to as transferability, is an important issue that remains to be carefully analyzed. Using the EC‐Earth GCM and focusing on precipitation, we assess the transferability of generalized linear models, convolutional neural networks and a posteriori random forests (APRFs). We conclude that APRFs present the best overall performance for the historical period, and future local climate change signals consistent with those projected by EC‐Earth. Moreover, we show how a slight modification of APRFs can greatly improve the temporal consistency of the downscaled series.