Comparison of ARIMA Parameter Estimation Using Maximum Likelihood and Bayesian with Gamma Distribution on IHSG Data

Abstract

This study aims to examine the differences in the parameter estimation results of the ARIMA(0,1,2) model with Gamma-distributed residuals using two statistical approaches, namely Maximum Likelihood (ML) and Bayesian. The ML estimation results show that the parameters MA(1) ≈ 0.0028 and MA(2) ≈ 0.0370 are very small, indicating that the influence of the previous residuals on daily JCI changes is relatively weak after the differencing process. The Gamma shape parameter of 3.7368 reflects residuals that tend to be symmetrical. The Neg Log-Likelihood value of 1350.98 produces an AIC of 2707.96 as an indicator of model fit. In contrast, the Bayesian approach provides estimates of MA(1) ≈ 0.25 and MA(2) ≈ 0.15 which are larger than ML, reflecting estimates that consider parameter uncertainty through the posterior distribution. The resulting Gamma parameters (α ≈ 3, β ≈ 0.015) show positive residual characteristics with moderate variations.