Motivated by the fact that many physical systems display (i) power-law correlations together with (ii) an asymmetry in the probability distribution, we propose a stochastic process that can model both properties. The process depends on only two parameters, where one controls the scaling exponent of the power-law correlations, and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected. We apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data.