The downward trend in Arctic sea ice is a key factor determining the pace and intensity of future global climate change; moreover, declines in sea ice can have a wide range of additional environmental and economic consequences. Based on several decades of satellite data, we provide statistical forecasts of Arctic sea ice extent during the rest of this century. The best fitting statistical model indicates that sea ice is diminishing at an increasing rate. By contrast, average projections from the CMIP5 global climate models foresee a gradual slowing of sea ice loss even in high carbon emissions scenarios. Our long-range statistical projections also deliver probability assessments of the timing of an ice-free Arctic. This analysis indicates almost a 60 percent chance of an effectively ice-free Arctic Ocean in the 2030s – much earlier than the average projection from global climate models.