PREDICTION THE ARCH GARCH APPROACH AND THE FOURIER SERIES

Abstract

The Indonesia Composite Index (ICI) is a key indicator of stock market performance in Indonesia, often experiencing high volatility due to various domestic and global economic factors. In recent years, ICI has shown a significant upward trend, influenced by both local and international factors. In 2024, from June to October, the ICI saw a notable increase, reaching its highest value since 2020 at Rp 7,670. Despite fluctuations in stock prices, the rise in ICI reflects a positive outlook for the Indonesian stock market, attracting both domestic and foreign investors. This study aims to predict ICI movements using ARIMA-GARCH and Fourier Series approaches. The ARIMA model is employed to analyze time series data, while the ARCH-GARCH model addresses heteroskedasticity in residual variance. For comparison, the Fourier Series Estimator is applied to capture seasonal patterns in the data. Although ICI volatility is driven by a range of external macroeconomic and geopolitical factors, this study focuses on univariate modeling to evaluate the predictive capability of the index’s own historical movements, without involving exogenous variables. The data used comes from Investing.com. Weekly ICI data from March 2020 to June 2024 is used, split into training and testing sets. The analysis results indicate that the ARIMA-GARCH method provides higher accuracy, with a Mean Absolute Percentage Error (MAPE) of 5% (out-sample), compared to the Fourier Series method, which has a MAPE of 8.57%. This suggests that ARIMA-GARCH is more effective in predicting ICI trends, reflecting its ability to account for volatility and market changes more accurately.