Nurul Hila Zainuddin, Muhamad Safiih Lola, Maman Abdurachman Djauhari, Fadhilah Yusof, Mohd Noor Afiq Ramlee, Aziz Deraman, Yahaya Ibrahim, Mohd Tajuddin Abdullah
Hybrid models such as the Artificial Neural Network-Autoregressive Integrated Moving Average (ANN–ARIMA) model are widely used in forecasting. However, inaccuracies and inefficiency remain in evidence. To yield the ANN–ARIMA with a higher degree of accuracy, efficiency and precision, the bootstrap and the double bootstrap methods are commonly used as alternative methods through the reconstruction of an ANN–ARIMA standard error. Unfortunately, these methods have not been applied in time series-based forecasting models. The aims of this study are twofold. First, is to propose the hybridization of bootstrap model and that of double bootstrap mode called Bootstrap Artificial Neural Network-Autoregressive Integrated Moving Average (B-ANN–ARIMA) and Double Bootstrap Artificial Neural Network-Autoregressive Integrated Moving Average (DB-ANN–ARIMA), respectively. Second, is to investigate the performance of these proposed models by comparing them with ARIMA, ANN and ANN–ARIMA. Our investigation is based on three well-known real datasets, i.e., Wolf's sunspot data, Canadian lynx data and, Malaysia ringgit/United States dollar exchange rate data. Statistical analysis on SSE, MSE, RMSE, MAE, MAPE and VAF is then conducted to verify that the proposed models are better than previous ARIMA, ANN and ANN–ARIMA models. The empirical results show that, compared with ARIMA, ANNs and ANN–ARIMA models, the proposed models generate smaller values of SSE, MSE, RMSE, MAE, MAPE and VAF for both training and testing datasets. In other words, the proposed models are better than those that we compare with. Their forecasting values are closer to the actual values. Thus, we conclude that the proposed models can be used to generate better forecasting values with higher degree of accuracy, efficiency and, precision in forecasting time series results becomes a priority. © 2019 Elsevier B.V.
Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak, 35900, Malaysia; Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, 21030, Malaysia; Graduate School, Universitas Pendidikan Indonesia, Bandung, 40154, West Java, Indonesia; Faculty of Science, Universiti Teknologi Malaysia, Skudai, Johor, 81310, Malaysia; Institute of Tropical Biodiversity and Sustainable Development, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, 21030, Malaysia; Faculty of Applied Social Science, University Sultan Zainal Abidin, Kuala Nerus, Terengganu, 21030, Malaysia
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