Linear time series models are not able to capture the behaviour of many financial time series, as in the cases of exchange rates and stock market data. Some phenomena, such as volatility and structural breaks in time series data, cannot be modelled implicitly using linear time series models. Therefore, nonlinear time series models are typically designed to accommodate for such nonlinear features. In the present study, a nonlinearity test and a structural change test are used to detect the nonlinearity and the break date in three ASEAN currencies, namely the Indonesian Rupiah (IDR), the Malaysian Ringgit (MYR) and the Thai Baht (THB). The study finds that the null hypothesis of linearity is rejected and evidence of structural breaks exist in the exchange rates series. Therefore, the decision to use the self-exciting threshold autoregressive (SETAR) model in the present study is justified. The results showed that the SETAR model, as a regime switching model, can explain abrupt changes in a time series. To evaluate the prediction performance of SETAR model, an Autoregressive Integrated Moving Average (ARIMA) model used as a benchmark. In order to increase the accuracy of prediction, both models are combined with an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model. The prediction results showed that the construct model of SETAR-EGARCH performs better than that of the ARIMA model and the combined ARIMA and EGARCH model. The results indicated that nonlinear models give better fitting than linear models.