Long Memory and Hysteresis

The aim of this chapter is to determine whether the hysteretic series can be confused with long memory series, since the hysteretic effect is a persistence in the series like the long memory effect. Nevertheless, the long term behavior of the hysteretic series is very different from the long term behavior of the long memory series: the hysteretic series are not mean reverting whereas the long memory series are (if correctly differencied). Since the mean reverting property is crucial for many economic models for checking the stability of equilibria, distinguishing between hysteresis and long memory is very important. This difference is due to the fact that hysteresis models have in fact a short memory, since dominant shocks erase the memory of the series, and the persistence is due to permanent and nonreverting state changes at a microstructure level. For checking whether hysteretic series can display long memory property, a model possessing the hysteresis property is used for simulating hysteretic data. Statistical tests for short memory against long memory alternatives are applied to these simulated data.