Basak and Ho (2004) derived numerical formulas for the mean first passage time of ARMA models using the integral equation approach. Recently, the ESTAR model has become a popular model for the analysis of economic and financial data. Some researchers used the ESTAR model to analyze real exchange rates, purchasing power parity (PPP) deviations, and arbitrage processes. This article shows that under certain conditions, the integral equation approach can still be used for the ESTAR model. Numerical schemes of the mean first passage time for ESTAR(1) and ESTAR(2) models are proposed in this article. The applications of the schemes for real exchange rates between Australian and New Zealand dollars as well as for pairs trading following the ESTAR(1) model are provided. Copyright © Grace Scientific Publishing, LLC.