When modeling financial data, the Markov-switching GARCH model provides interesting dynamics. It is difficult to estimate this path dependence model since it is not practical to compute the likelihood exactly in practice. This has given rise to a plethora of numerical computing techniques for determining maximum likelihood. Several numerical techniques have been used to estimate the likelihood function, and similar techniques have been used by others to represent this path dependence model. In this study, exchange rate data were utilized to estimate the parameters of the Markov-switching GARCH model for single, two, and three regimes using the maximum likelihood (ML) and Bayesian method (BM) of estimation. Based on their information criteria, it was found that the three regimes switching GARCH model performed better for the ML approach than the other regime-switching model, while the two regimes switching performed better based on the deviance information criteria for the BM of estimate. Moreover, according to their information criterion, the ML outperformed the BM.