Hybrid MODWT-ARMA Model for Indonesia Stock Exchange LQ45 Index Forecasting

This research discussed a hybrid Maximal Overlap Discrete Wavelet Transform (MODWT)-Autoregressive Moving Average (ARMA) model by combining the MODWT and the ARMA models to deal with the nonstationary and long-range dependence (LRD) time series. Theoretically, the details series obtained by MODWT are stationary and short-range dependent (SRD). Then, the general form of the MODWT-ARMA model was derived. In the experimental study, the daily Indonesia stock exchange LQ45 index time series was used to assess the performance of the hybrid model. Finally, the Mean Squared Error (MSE) and Mean Absolute Percent Error (MAPE) comparison with DWT-ARMA, ARIMA, and exponential smoothing models indicates that this combined model effectively improves forecasting accuracy. Based on the result of the analysis, the score of MSE of the MODWT-ARMA model was 51.42533, the score of the DWT-ARMA model was 180.1799, the score of the ARIMA model was 168.7863, and the score of the exponential smoothing model was 168.7824. At the same time, the score of MAPE in the MODWT-ARMA model was 0.00580797, the score of the DWT-ARMA model was 0.01106721, the score of the ARIMA model was 0.01070074, and the score of the exponential smoothing model was 0.01069591.