Modeling the United States Unemployment Rate with the Preisach Model of Hysteresis

Abstract

A system with hysteresis is one that exhibits path dependent but rate independent memory. Hysteresis can be observed physically through the magnetization of a ferromagnetic material. In order to mathematically describe systems with hysteresis, we use the Preisach model. A discussion of the Preisach model is given as well as a method for computing the hysteretic transformation of an input variable. The focus of this paper is hysteresis in economics, namely, unemployment. We consider essential time series techniques for analyzing time series data, i.e. unit root testing for stationarity. However, we point out problems in modeling hysteresis with these techniques and argue that unit root tests cannot capture the selective memory of a system with hysteresis. For that, hysteresis in economic time series data is modeled using the Preisach model. We test the explanatory power of the previous unemployment rate on the current unemployment rate using both a hysteretic and non-hysteretic model. We find that the non-hysteretic model is better at explaining current unemployment rates, which suggests hysteresis is not present in the United States unemployment rate.