Penaksiran Parameter Model ARIMA dengan Metropolis-Hastings dan Gibbs Sampling

Abstract

The ARIMA model is one of the most widely used methods in time series analysis, particularly for forecasting. The accuracy of the ARIMA model strongly depends on precise parameter estimation. The aim of this study is to estimate the parameters of the ARIMA(1,1,1) model and to compare the performance of three estimation methods, namely Maximum Likelihood Estimation (MLE), Metropolis-Hastings (MH), and Gibbs Sampling (GS), using both simulated data and real stock data. The simulated data were generated with various sample sizes, including the addition of outliers, to assess the robustness of each method against extreme values. The results show that Gibbs Sampling provides the most accurate estimates for small samples, while MetropolisHastings performs better with medium-sized samples and real stock data, yielding the lowest prediction errors. MLE produces reliable results for normally distributed large samples, particularly due to its computational efficiency. These findings indicate that Bayesian approaches, especially Metropolis-Hastings, are more robust for parameter estimation of ARIMA models in real data and medium-sized samples, while Gibbs Sampling is particularly useful for small samples or data with outliers, and MLE remains effective for large and normally distributed datasets.