Applied Soft Computing Journal 84 (2019) 105676 Contents lists available at ScienceDirect Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc Improvement of time forecasting models using a novel hybridization of bootstrap and double bootstrap artificial neural networks Nurul Hila Zainuddin a , Muhamad Safiih Lola b,∗ , Maman Abdurachman Djauhari c , Fadhilah Yusof d , Mohd Noor Afiq Ramlee e , Aziz Deraman b , Yahaya Ibrahim f , Mohd Tajuddin Abdullah e a Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak, Malaysia b Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia c Graduate School, Institut Pendidikan Indonesia, Jl. Terusan Pahlawan 32, Garut, 44151, Indonesia d Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia e Institute of Tropical Biodiversity and Sustainable Development, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia f Faculty of Applied Social Science, University Sultan Zainal Abidin, 21030 Kuala Nerus, Terengganu, Malaysia article info Article history: Received 3 October 2018 Received in revised form 8 June 2019 Accepted 28 July 2019 Available online 12 August 2019 Keywords: Hybridization Double bootstrap Artificial neural networks ARIMA Accuracy and efficiency abstract 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. All rights reserved. 1. Introduction A time series is a sequence of observations over time which can be discrete or continuous over a time unit [1,2]. In a time series forecasting model, accuracy and efficiency are important criteria and have been the focus for many researchers. Such a model has been widely used particularly in the areas of eco- nomics, tourism, renewable energy, social analysis and, financial analysis, i.e., exchange rate, due to its ability to estimate time ∗ Corresponding author. E-mail address: safiihmd@umt.edu.my (M.S. Lola). series data accurately. The Autoregressive Integrated Moving Av- erage (ARIMA) has been evaluated in this regard [3–14] and the model has achieved popularity, even domination in time series forecasting. ARIMA is flexible and has been used to represent several different types of time series [2,15,16]. Generally, ARIMA assumes that a linear relationship exists between future values of a time series with both current past values and, white noise [2]. However, for complex real-world problems, approximations by ARIMA models are inadequate in representing a barrier in time series forecasting for researchers. Therefore, various methods and approaches are needed which work outside the restriction of a linear relationship. The use of hybrid forecasting models using ANNs with auto- regressive integrated moving average (ARIMA) in execution of https://doi.org/10.1016/j.asoc.2019.105676 1568-4946/© 2019 Elsevier B.V. All rights reserved.