Forecasting PT Pertamina Geothermal Energy TBK (PGEO) Share Prices using the Arch-Garch Model - Ramadhan, Ramadhan; Yurinanda, Sherli; Sarmada, Sarmada (Jurusan Matematika FMIPA UNM, 2025)
This study focuses on forecasting the daily closing price of PT Pertamina Geothermal Energy Tbk (PGEO) stocks, recognizing the non-stationary and volatile nature of financial time series data. Traditional forecasting methods, such as the ARIMA (Autoregressive Integrated Moving Average) model, are often insufficient for such data because they rely on the assumption of homoscedasticity, or constant variance in the residuals. An analysis of PGEO's daily stock prices from November 2023 to July 2024 revealed significant fluctuations, indicating the presence of heteroscedasticity, where the variance of the residuals is not constant. In tackling this problem, the study utilized the ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) frameworks, purpose-built to identify and model the phenomenon of volatility clustering within financial datasets. By integrating the ARIMA model with GARCH, the study aimed to create a more robust forecasting tool. After testing various combinations, the MA(1)–GARCH(1,1) model was identified as the most suitable for predicting PGEO's stock prices. This model successfully captured the fluctuating volatility and produced a highly accurate forecast, as evidenced by a Mean Absolute Percentage Error (MAPE) of just 2.97%. A MAPE value below 10% is generally considered to represent a very high level of forecasting accuracy, confirming the effectiveness of the chosen model in providing reliable short-term predictions for stock market movements. Keywords: ARCH-GARCH, Stock price forecasting, ARIMA