The hysteresis terminology has mainly been used in two fields of economics, unemplyment and international trade, with a different meaning however, involving either linear autoregressive macro behaviour or non- linear heterogenous mico behaviour. There may nonetheless be observational equivalence between the 'persistence' characterising unit- root processes and the 'remanence' created by the aggregation of non- linear dynamics. Stochastic simulations are employed to analyse the properties of the output of an hysteretic system, subject to white noise and random walk inputs. Non-linear hysteretic systems are found to generate a sizeable proportion - two-thirds - of stationary output from stationary input, and to possibly generate an output cointegrated with the corresponding input. Such processes therefore appear significantly different from an integrated process. This stresses the specific relevance of a non-linear approach to hysteresis.