A test statistic for nonlinearity of a given heavy-tailed time series process is constructed, based on the sub-sample stability of Gini-based sample autocorrelations. The finite-sample performance of the proposed test is evaluated in a Monte Carlo study and compared to a similar test based on the sub-sample stability of a heavy-tailed analogue of the conventional sample autocorrelation function. In terms of size and power properties, the quality of our test outperforms a nonlinearity test for heavy-tailed time series processes proposed by [S.I. Resnick and E. Van den Berg, A test for nonlinearity of time series with infinite variance , Extremes 3 (2000), pp. 145-172.]. A nonlinear Pareto-type autoregressive process and a nonlinear Pareto-type moving average process are used as alternative specifications when comparing the power of the proposed test statistic. The efficacy of the test is illustrated via the analysis of a heavy-tailed actuarial data set and two time series of Ethernet traffic.