Empirical study on the HMM of nonlinear nominal exchange rates

The exchange rate model for the study of the exchange rate theory has very important significance. After analyzing the successful nonlinear model of real exchange rate based on the purchasing power parity (PPP) theory, the nonlinear problem of nominal exchange rate is studied in this paper. Through a research on a period of nominal exchange rate with nonlinear characteristics, a nonlinear statistical model of nominal exchange rate based on the hidden Markov model (HMM) is proposed, and the parameters of the model are estimated. Hypothesis testing shows that the model can accurately describe the statistical characteristics of the nominal exchange rate time series. The parameters showed that the nominal exchange rate model proposed in this paper, to some extent, supports that deviations from purchasing power parity (PPP) are nonlinear mean reversions.