Cryptocurrencies became one of the main trends in modern economy. However by the moment the forecast of cryptocurrencies values is an open problem, which is almost non-reflected in publications related to finance market. Reasons consist in its novelty, large volatility and its strong dependence on subjective factors. In this experimental research we show possibilities of GMDH-technology to give weekly and monthly forecast for values of cryptocurrency 'Waves' (waves/euro rate). The source information is week data covering the period 2017-2019. We tests 4 algorithms from the GMDH Shell platform on the whole period and on the crisis period 4-th quarter 2017 – 2nd quarter 2018. Baseline is provided by the popular statistical method of double exponential smoothing. The results of Pilot study can be considered as the very promising ones having in view the large variability of data.