Over the years, maximum likelihood estimation and Bayesian method became popular statistical tools in which applied to fit finite mixture model. These trends begin with the advent of computer technology during the last decades. Moreover, the asymptotic properties for both statistical methods also act as one of the main reasons that boost the popularity of the methods. The difference between these two approaches is that the parameters for maximum likelihood estimation are fixed, but unknown meanwhile the parameters for Bayesian method act as random variables with known prior distributions. In the present paper, both the maximum likelihood estimation and Bayesian method are applied to investigate the relationship between exchange rate and the rubber price for Malaysia, Thailand, Philippines and Indonesia. In order to identify the most plausible method between Bayesian method and maximum likelihood estimation of time series data, Akaike Information Criterion and Bayesian Information Criterion are adopted in this paper. The result depicts that the Bayesian method performs better than maximum likelihood estimation on financial data.