Three-regime mean reversion, TAR and its application

Abstract

This paper, for the first time, defined the three-regime mean reversion, which is used to describe a special mean reversion phenomenon and to explain the non-linear mean reversion and short-term "non-stationary" phenomenon of time series. Threshold autoregressive model (TAR) and regime-switching model (RSM) can be used to model the three-regime mean reversion. As an empirical example, this paper used three-regime threshold autoregressive model to fit the log growth rate of China's trade surplus with the United States and Hong Kong. The empirical results showed that during the past ten years the probability of the above growth rate in high-level mean process (expansion) is over 50%. The average growth rate is lowest in recession and highest in expansion. The properties of the mean reversion process are characterized by a higher constant term in low-level mean process equation but the lower slope coefficient and a lower constant term in high-level mean process equation but the relatively higher slope coefficient. Therefore, the three-regime TAR model can be used to model three-regime mean reversion phenomenon.