Abstract
Literature indicates that many efforts have been conducted toward the development of forecasting models with a high degree of accuracy. Combining different models is known as a powerful alternative to access more reliable and more accurate results than single models. Given the great importance of hybridization theory, various hybrid models have been proposed in the literature of time series forecasting. Series hybrid approaches are one of the most well study and the most widely used hybridization models, in which components are sequentially applied. However, according to the modeling essence of this hybrid structure, the performance of the series hybrid models is directly dependent on the order of using components and modeling sequence. Besides, selecting the best modeling order that can yield the best performance in all situations is a problematic theoretical as well as practical task. Thus, the main purpose of this paper is to eliminate the drawback of series models, regarding modeling order selection using a parallel hybridization schema, which is addressed for the first time. The core principle of the proposed parallel hybridization of series (PHOS) models is to improve the series hybrid model’s forecasting accuracy by integrating two hybrid structures in contrast to existing hybrid models, which emphasize only the combination of individual models. The proposed model decomposes the original time series into two linear and nonlinear parts and uses the autoregressive integrated moving average (ARIMA) and multilayer perceptron neural network (MLP) models to model underlying patterns, incorporating two series models including ARIMA–MLP and MLP–ARIMA. Finally, the series models are integrated as components of the parallel hybridization scheme. Moreover, an ordinary least square algorithm is developed to determine the optimal weights of these two components. Three benchmark data sets, including the closing of the DAX index, the closing of the Nikkei 225 index (N225), and the opening of the Dow Jones Industrial Average Index, are used for empirical analysis and verifying the effectiveness of the PHOS model. The empirical analysis indicates that the PHOS model can improve the forecasting performance of both series ARIMA–MLP and MLP–ARIMA models as well as individual models and some parallel hybrid models.
Similar content being viewed by others
References
Amini MH, Kargarian A, Karabasoglu O (2016) ARIMA-based decoupled time series forecasting of electric vehicle charging demand for stochastic power system operation. Electr Power Syst Res 140:378–390
Armaghani DJ, Shoib RS, Faizi K, Safuan A, Rashid A (2017) Developing a hybrid PSO–ANN model for estimating the ultimate bearing capacity of rock-socketed piles. Neural Comput Appl 28:391–405
Armstrong JS (2001) Principles of forecasting—a handbook for researchers and practitioners. Kluwer Academic Publishers, Berlin
Barak S, Sadegh SS (2016) Forecasting energy consumption using ensemble ARIMA–ANFIS hybrid algorithm. Electr Power Energy Syst 82:92–104
Bates JM, Granger CWJ (1969) The combination of forecasts. Oper Res Q 20:451–468
Box GP, Jenkins GM (1976) Time series analysis: forecasting and control. Holden-Day, San Francisco
Bunn D (1989) Forecasting with more than one model. J Forecast 8:161–166
Büyükşahin ÜÇ, Ertekin Ş (2019) Improving forecasting accuracy of time series data using a new ARIMA-ANN hybrid method and empirical mode decomposition. Neurocomputing 361:151–163
Chakraborty T, Chattopadhyay S, Ghosh I (2019) Forecasting dengue epidemics using a hybrid methodology. Phys A Stat Mech Appl 527:121266
Chen J, Zeng GQ, Zhou W, Du W, Lu KD (2018) Wind speed forecasting using nonlinear-learning ensemble of deep learning time series prediction and extremal optimization. Energy Convers Manag 165:681–695
Chouikhi N, Ammar B, Rokbani N, Alimi AM (2017) PSO-based analysis of echo state network parameters for time series forecasting. Appl Soft Comput 55:211–225
Clemen RT (1989) Combining forecasts: a review and annotated bibliography. Int J Forecast 5:559–583
do Camelo HN, Lucio PS, Junior JBVL, de Carvalho PCM, dos Santos DVG (2018) Innovative hybrid models for forecasting time series applied in wind generation based on the combination of time series models with artificial neural networks. Energy 151(347–357):2018
Granger CWJ, Ramanathan R (1984) Improved methods of combining forecasts. J Forecast 3:197–204
Hafezi R, Shahrabi J, Hadavandi E (2015) A bat-neural network multi-agent system (BNNMAS) for stock price prediction: case study of DAX stock price. Appl Soft Comput 29:196–210
Kao L-J, Chiu C-C, Lu C-J, Chang C-H (2013) A hybrid approach by integrating wavelet-based feature extraction with MARS and SVR for stock index forecasting. Decis Support Syst 54:1228–1244
Khashei M, Bijari M (2011) A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Appl Soft Comput 11:2664–2675
Khashei M, Bijari M, Ardali GAR (2012) Hybridization of autoregressive integrated moving average (ARIMA) with probabilistic neural networks (PNNs). Comput Ind Eng 63:37–45
Liu Z, Wang X, Zhang Q, Huang C (2018a) Empirical mode decomposition based hybrid ensemble model for electrical energy consumption forecasting of the cement grinding process. Measurement 138:314–324
Liu H, Mi X, Li Y (2018b) Comparison of two new intelligent wind speed forecasting approaches based on wavelet packet decomposition, complete ensemble empirical mode decomposition with adaptive noise and artificial neural networks. Energy Convers Manag 155:188–200
Mehdizadeh S, Fathian F, Adamowski JF (2019) Hybrid artificial intelligence-time series models for monthly streamflow modeling. Appl Soft Comput 80:873–887
Meshram SG, Ghorbani MA, Shamshirband S, Karimi V, Meshram C (2019) River flow prediction using hybrid PSOGSA algorithm based on feed-forward neural network. Soft Comput 23:1–10
Moeeni H, Bonakdari H (2017) Forecasting monthly inflow with extreme seasonal variation using the hybrid SARIMA-ANN model. Stoch Environ Res Risk Assess 31:1997–2010
Mohan N, Soman KP, Sachin Kumar S (2018) A data-driven strategy for short-term electric load forecasting using dynamic mode decomposition model. Appl Energy 232:229–244
Panigrahi S, Behera HS (2017) A hybrid ETS–ANN model for time series forecasting. Eng Appl Artif Intell 66:49–59
Panigrahi S, Behera HS (2019) An adaptive fuzzy filter-based hybrid ARIMA–HONN model for time series forecasting. In: Computational intelligence in data mining, pp 841–850
Pradeepkumar D, Ravi V (2017) Forecasting financial time series volatility using particle swarm optimization trained quantile regression neural network. Appl Soft Comput 58:35–52
Qiu X, Ren Y, Suganthan PN, Amaratunga GAJ (2017a) Empirical mode decomposition based ensemble deep learning for load demand time series forecasting. Appl Soft Comput 54:246–255
Qiu X, Zhang L, Suganthan PN, Amaratunga GAJ (2017b) Oblique random forest ensemble via least square estimation for time series forecasting. Inf Sci 420:249–262
Ribeiro GT, Mariani VC, dos Santos Coelho L (2019) Enhanced ensemble structures using wavelet neural networks applied to short-term load forecasting. Eng Appl Artif Intell 82:272–281
Sarıca B, Eğrioğlu E, Aşıkgil B (2018) A new hybrid method for time series forecasting: A.R.–ANFIS. Neural Comput Appl 29:749–760
Singh PK, Singh N, Negi R (2019) Wind power forecasting using hybrid ARIMA–ANN technique. In: Ambient communications and computer systems, pp 209–220
Song G, Dai Q (2017) A novel double deep ELMs ensemble system for time series forecasting. Knowl Based Syst 134:31–49
Suhermi N, Prastyo DD, Ali B (2018) Roll motion prediction using a hybrid deep learning and ARIMA model. Proc Comput Scis 144:251–258
Sun S, Wang S, Zhang G, Zheng J (2018) A decomposition-clustering-ensemble learning approach for solar radiation forecasting. Sol Energy 163:189–199
Voronin S, Partanen J (2014) Forecasting electricity price and demand using a hybrid approach based on wavelet transform, ARIMA and neural networks. Int J Energy Res 38:626–637
Wang J, Li Y (2019) An innovative hybrid approach for multi-step ahead wind speed prediction. Appl Soft Comput 78:296–309
Wang JJ, Wang J-Z, Zhang ZG, Guo S-P (2012) Stock index forecasting based on a hybrid model. Omega 40:758–766
Wang WCH, Chau KW, Qiu L, Chen YB (2015) Improving forecasting accuracy of medium and long-term run off using artificial neural network based on EEMD decomposition. Environ Res 139:46–54
Wang Z, Zeng YR, Wang S, Wang L (2019) Optimizing echo state network with backtracking search optimization algorithm for time series forecasting. Eng Appl Artif Intell 81:117–132
Wei LY (2016) A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting. Appl Soft Comput 42:368–376
Wu J, Cui Z, Chen Y, Kong D, Wang YG (2019) A new hybrid model to predict the electrical load in five states of Australia. Energy 166:598–609
Xiao L, Shao W, Yu M, Ma J, Jin C (2017) Research and application of a hybrid wavelet neural network model with the improved cuckoo search algorithm for electrical power system forecasting. Appl Energy 198:203–222
Xiong T, Li C, Bao Y (2017) Interval-valued time series forecasting using a novel hybrid HoltI and MSVR model. Econ Model 60:11–23
Yang HF, Chen YPP (2019) Hybrid deep learning and empirical mode decomposition model for time series applications. Expert Syst Appl 120:128–138
Yang Z, Ce L, Lian L (2017) Electricity price forecasting by a hybrid model, combining wavelet transform, ARMA and kernel-based extreme learning machine methods. Appl Energy 190:291–305
Yu L, Xu H, Tang L (2017) LSSVR ensemble learning with uncertain parameters for crude oil price forecasting. Appl Soft Comput 56:692–701
Yu C, Li Y, Xiang H, Zhang M (2018) Data mining-assisted short-term wind speed forecasting by wavelet packet decomposition and Elman neural network. J Wind Eng Ind Aerodyn 175:136–143
Zameer A, Arshad J, Khan A, Raja MAZ (2017) Intelligent and robust prediction of short term wind power using genetic programming based ensemble of neural networks. Energy Convers Manag 134:361–372
Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175
Zhu B, Han D, Wang P, Wu Z, Zhang T, Wei YM (2017) Forecasting carbon price using empirical mode decomposition and evolutionary least squares support vector regression. Appl Energy 191:521–530
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
Author Zahra Hajirahimi declares that she has no conflict of interest. Author Mehdi Khashei declares that he has no conflict of interest.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hajirahimi, Z., Khashei, M. Parallel hybridization of series (PHOS) models for time series forecasting. Soft Comput 25, 659–672 (2021). https://doi.org/10.1007/s00500-020-05176-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-020-05176-0