A Hybrid MODWT-ARIMA-FFNN Framework for Capturing Linear and Non-linear Patterns in ISSI Time Series

Abstract

Time series forecasting plays a crucial role in data-driven decision-making, particularly in the financial context. Various forecasting methods, such as ARIMA, Neural Networks (NN), and Wavelet Transforms, have different advantages and limitations in handling linear and non-linear patterns. This study compares the forecasting performance of ARIMA, Feedforward Neural Network (FFNN), and the hybrid MODWT-ARIMA-FFNN model, referred to as MODWT, developed to enhance prediction accuracy. The novelty of the hybrid framework lies in its structure, where MODWT decomposes the time series into detail and smooth components, ARIMA forecasts the detail components, and FFNN models the smooth component before reconstructing the final forecast. The dataset consists of 237 observations from the Indonesian Sharia Stock Index (ISSI) between September 4, 2017, and September 19, 2018, divided into 225 training points and 12 testing points. Model performance is evaluated using Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). The results indicate that the hybrid MODWT model outperforms ARIMA and FFNN individually, achieving the lowest testing errors with MSE equal to 2.3735 and MAPE equal to 0.0075. The model effectively captures both linear and non-linear patterns, making it particularly suitable for financial forecasting where data complexity and variability are high. Its performance demonstrates the potential of the hybrid MODWT framework for broader applications in forecasting financial markets and other sectors involving complex, non-linear time series data.