Demographic compensation arises when vital rates change in opposite directions across populations,  buffering the variation in population growth rates, and is a mechanism often invoked to explain the  stability of species geographic ranges. However, studies on demographic compensation have disregarded  the effects of temporal variation in vital rates and their temporal correlations, despite theoretical  evidence that stochastic dynamics can affect population persistence in temporally varying environments.  We carried out a seven-year-long demographic study on the perennial plant Arabis alpina across six  populations encompassing most of its elevational range. We discovered demographic compensation in  the form of negative correlations between the means of plant vital rates, but also between their  temporal coefficients of variation, correlations and elasticities. Even if their contribution to demographic  compensation was small, this highlights a previously overlooked, but potentially important, role of  stochastic processes in stabilizing population dynamics at range margins.