Application of Heuristic Rules and Genetic Algorithm in ARMA Model Estimation for Time Series Prediction

Document Type: Research Paper

Authors

1 Assistant Prof./ Allameh Tabataba'i University

2 student/Allameh Tabataba'i University

Abstract

The first step of forecasting time series is to build an appropriate model. Determining orders and estimation of ARMA model parameters is a challenging field in traditional statistical and intelligent methods. In this paper, genetic algorithm is used for parameter estimation and heuristic rules are used to determine orders of ARMA model. Heuristic rules are extracted according to time series properties. The data are selected using sliding time window. Model identification is carried out by using Bayesian information criterion (BIC). The mean squares error and the mean absolute percentage error are used to evaluate the results of prediction. The proposed method was applied to eight time series in different types, and the results were compared with results of statistical methods. The achieved result shows equivalent or superior performance for the proposed method in comparison with the classic method.

Keywords

Main Subjects


Bäck, T. (1996). Evolutionary Algorithms in Theory and Practice. Oxford University Press.

Beheshti-Nia, M.A. & Farazmand, N. (2015). A Novel Decision Support System for Discrete Cost-CO2 Emission Trade-off in Construction Projects: The Usage of Imitate Genetic Algorithm. Journal of information technology management, 7(1): 23-48. (in Persian)

Beligiannis, G.N., Likothanassis, S.D. & Demiris, E.N. (2001) A robust hybrid evolutionary method for ARMA model identification. in Image and Signal Processing and Analysis. ISPA 2001. Proceedings of the 2nd International Symposium on.

Boularouk, Y. & Djeddour, K. (2015). New approximation for ARMA parameters estimate. Mathematics and Computers in Simulation, 118: 116–122.

Box, G. & G. Jenkins. (1976). Time Series Analysis: Forecasting and Control. Holden Day, San Francisco, USA.

 

Chao-Ming, H. & Hong-Tzer, Y. (1995). A time series approach to short term load forecasting through evolutionary programming structures. in Energy Management and Power Delivery. Proceedings of EMPD '95, 1995 International Conference on.

Conner, J.T., Martin, R.D & Atlas, L.E. (1994). Recurrent neural networks and robust time series prediction. Neural Networks, IEEE Transactions, 5(2): 240- 254.

Cortez, P., Rocha, M. & Neves, J. (2004). Evolving Time Series Forecasting ARMA Models. Journal of Heuristics, 10(4): 415-429.

Cortez, P., M. Rocha, and J. Neves. (2001). Genetic and Evolutionary Algorithms for Time Series Forecasting. In Monostori, L., V´ancza, J., and Alis, M. (eds.), Engineering of Intelligent Systems: Proc. of IEA/AIE 2001, LNAI 2070: 393-402.

De Gooijer, G.J. & Hyndman, R. J. (2006). 25 years of time series forecasting. International Journal of Forecasting, 22(3): 443-473.

Elahi, S., Rashidi, M. & Sadeghi, M. (2015). Designing fuzzy expert system for chief privacy officer in government and businesses E-transactions. Journal of information technology management. 7(3): 511-530. (in Persian)

Flores, J. & Graff, M. (2012). Evaluative design of ARMA and ANN models for time series forecasting. Renewable Energy, 44: 225-230.

Ghasemi, A.R. & Asgharizadeh, E. (2014). Presenting a Hybrid ANN-MADM Method to Define Excellence Level of Iranian Petrochemical Companies. Journal of information technology management, 6(2): 267-284. (in Persian)

Graves, D. & Pedrycz, W. (2009). Fuzzy prediction architecture using recurrent neural networks. Neurocomputing, 72(9): 1668-1678.

Hamzaçebi, C., Akay, D. & Kutay, F. (2009). Comparison of direct and iterative artificial neural networks forecast approaches in multi-periodic time series forecasting, Expert Systems with Applications, 36(2): 3839-3844.

Huang, Ch. & Yang, H. (1995). A time series approach to short term load forecasting through evolutionary programming structures. Energy Management and Power Delivery. Proceedings of EMPD 95. International Conference, 21-23 Nov. DOI: 10.1109/EMPD.1995. 500792.

Hyndman, R.J. & Koehler, A.B. (2006). Another look at measurs of forecast        accuracy. International Journal of Forecasting. 22(4): 679-688.

Ismail, Z. & Fong Yeng, F. (2011). Genetic Algorithm for Parameter Estimation in Double Exponential Smoothing. Australian Journal of Basic and Applied Sciences, 5(7): 1174-1180.

 

Karim, T. (2014). Desining an Expert System for Analyzing the Energy Consumption Behavior of Employees in Organizations Using Rough Set Theory. Journal of information technology management, 7(2): 363-384.
(in Persian)

Majhi, R., Majhi, B., Rout, M., Mishra, S. & Panda, G. (2009). Efficient sales forecasting using ARMA-PSO model. In: Proc. of IEEE International Conference on Nature and Biologically Inspired, Computing, pp. 1333–1337.

Makridakis, S., Weelwright, S. & Hyndman, R. (1998). Forecasting: Methods and Applications, 3rd edn. New York, USA: John Wiley & Sons.

Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. USA: Springer-Verlag.

Mohammadi, K. & Eslami, H.R. (2006). Parameter estimation of an ARMA model for river flow forecasting using goal programming. Journal of Hydrology, 331(1-2): 293– 299.

Oscar, C. & Patricia, M. (2002). Hybrid intelligent systems for time series prediction using neural networks, fuzzy logic, and fractal theory. Neural Networks, IEEE Transaction, 13(6): 1395-1408.

Oskoei, M.A. (2004). Time Series Prediction Using Neural Networks, Journal of Economic Research, 16(47): 163-183. (in Persian)

Oskoei, M.A. (2015). Application of Sliding Window for Financial Time Series Prediction using Time-Delay Neural Networks. Journal of Economic Research, ISSN: 1735-210X. (in Persian)

Panagiotopoulos, A. (2012). Optimizing Time Series Forecast Through Linear Programming. PhD Thesis, Nottingham University.

Rolf, S. & Sprave, J. (1997). Model identification and parameter estimation Of ARMA models by means of evolutionary algorithms. Computational Intelligence for Financial Engineering, 237(243): 23-25.

Rout, M. & Majhi, B. (2013). Forecasting of currency exchange rates using an adaptive ARMA model with differential evolution based training. Journal of King Saud University–Computer and Information Sciences, 26(1): 7–18.

Sapankevych, N.I. & Ravi, S. (2009). Time Series Prediction Using Support Vector Machines: A Survey. Computational Intelligence Magazine, IEEE, 4(2): 24-38.

Su, Z. & Wang, J. (2014). A new hybrid model optimized by an intelligent optimization algorithm for wind speed forecasting. Energy Conversion and Management, 85: 443-452.

Taghavi Fard, M.T., Hosseini, F. & Khanbabaei, M. (2014). Hybrid credit scoring model using genetic algorithms and fuzzy expert systems Case study: Ghavvamin financial and credit institution. Journal of information technology management,. 6(1): 31-46. (in Persian)

Ursem, R.K. & Vadstrup, P. (2003). Parameter Identification of Induction Motors Using Differential Evolution. Evolutionary Computation, CEC '03. The 2003 Congress 2: 8-12.

Van Gestel, T., Suykens, J.A.K., Baestaens, D.E., Lamberechts, A., Lanckriet, G., Vandaeie, B., DeMoor, B. & Vandewalle, J. (2001). Financial time series prediction using least squares support vector machines within the evidence framework. Neural Network, IEEE Transaction, 12(4): 809-821.

Vosough, M., Taghavi Fard, M.T. & Alborzi, M. (2015). Bank card fraud detection using artificial neural network. Journal of information technology management, 6(4): 721-746. (in Persian)

Wang, J. & Liang, J. (2008). ARMA Model identification using Particle Swarm Optimization Algorithm. ICCSIT, Computer Science and Information Technology, International Conference, 223-227.

White, M. & Wen, J. (2015). Optimal Estimation of Multivariate ARMA Models. AAAI Conference on Artificial Intelligence, North America.

Zhang, J., Chung, H.S.H. & Lo, W.L. (2008). Chaotic Time Series Prediction Using a Neuro-Fuzzy System with Time-Delay Coordinates. Knowledge and Data Engineering, IEEE Transactions, 20(7): 956-964.