This study aims to forecast extreme fluctuations of Bitcoin returns. Bitcoin is the first decentralized and the largest, in terms of capitalization, cryptocurrency. A well-timed and precise forecast of extreme changes in Bitcoin returns is key to market participants since they may trigger large-scale selling or buying strategies that may crucially impact the cryptocurrency markets. We term the instances of extreme Bitcoin movement as ‘spikes’. In this paper, spikes are defined as the returns instances that outreach a two-standard deviations band around the mean value. Instead of the unconditional historic standard deviation that is usually used, in this paper, we utilized a GARCH(p,q) model to derive the conditional standard deviation. We claim that the conditional standard deviation is a more suitable measure of on-the-spot risk than the overall standard deviation. The forecasting operation was performed using the support vector machines (SVM) methodology from machine learning. The most accurate forecasting model that we created reached 79.17% out-of-sample forecasting accuracy regarding the spikes cases and 87.43% regarding the non-spikes ones.