Modeling and forecasting abnormal stock returns using the nonlinear Grey Bernoulli model


  • Bahar Doryab Ferdowsi University of Mashhad, Mashhad, Iran
  • Mahdi Salehi


Abnormal returns, Gray theory, Nash nonlinear gray Bernoulli model, Nonlinear gray Bernoulli model


Purpose. This study aims to use gray models to predict abnormal stock returns.

Design/methodology/approach. Data are collected from listed companies in the Tehran Stock Exchange during 2005-2015. The analyses portray three models, namely, the gray model, the nonlinear gray Bernoulli model and the Nash nonlinear gray Bernoulli model.

Findings. Results show that the Nash nonlinear gray Bernoulli model can predict abnormal stock returns that are defined by conditions other than gray models which predict increases, and then after checking regression models, the Bernoulli regression model is defined, which gives higher accuracy and fewer errors than the other two models.

Originality/value. The stock market is one of the most important markets, which is influenced by several factors. Thus, accurate and reliable techniques are necessary to help investors and consumers find detailed and exact ways to predict the stock market.



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Abbasi, E. and Bagheri, S. (2011), “Predict stock returns using nonlinear models and the role of turnover in improving the performance of these models”, Journal of Financial Research, Vol. 13 No. 32, pp. 91-108.

Beneish, M.D. and Vargus, M.E. (2002), “Insider trading, earnings quality and accrual mispricing”, The Accounting Review, Vol. 77 No. 4, pp. 755-791.

Bhattacharyya, N. and Thomas, R.G. (2006), “Why people choose negative expected return assets - An empirical examination of a utility theoretic explanation”, Working paper, Federal Reserve Bank of St. Louis, available at: (accessed 20 March 2015).

Binder, J. (1998), “The event study methodology since 1969”, Review of Quantitative Finance and Accounting, Vol. 11 No. 2, pp. 111-137.

Bommer, E., Musumeci, J. and Poulsen, A. (1991), “Event-study methodology conditions of event induced variance”, Journal of Financial Economics, Vol. 30 No. 2, pp. 253-272.

Bozorgasl, M. and Sahebqarani, A. (2013), “Abnormal returns based on the model-based forecasts and industry momentum profits in Tehran stock exchange”, Experimental Studies Quarterly of Financial Accounting, Vol. 38, pp. 53-67.

Brown, S.J. and Warner, J.B. (1980), “Measuring security price performance”, Journal of Financial Economics, Vol. 8 No. 3, pp. 205-258.

Campbell, J.P. and Wiernik, B.W. (2015), “The modeling and assessment of work performance”, Annual Review of Organizational Psychology and Organizational Behavior, Vol. 2 No. 1, pp. 47-74.

Chan, K., Chan, L.K.C., Jegadeesh, N. and Lakonishok, J. (2006), “Earnings quality and stock returns”, The Journal of Business, Vol. 79 No. 3, pp. 1041-1082.

Chun, C., Hsin, P. and Wu, C. (2010), “Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model”, Expert Systems with Applications, Vol. 37 No. 12, pp. 7557-7562.

Deng, J. (1982), “Grey control system”, Journal of Huazhong University of Science and Technology, Vol. 3, pp. 9-18.

Dong, G., Yamaguchi, D. and Nagai, M. (2006), “A grey-based decision making approach to the supplier selection problem”, Mathematical and Computer Modeling, Vol. 46, pp. 573-581.

Hesin, P.H. and Chen, C.I. (2014), “The evolution of grey forecasting and its application on stock price prediction”, J Stock Forex Trad, Vol. 3, p. 124.

Huang, K. and Jane, C. (2009), “A hybrid model for stock market forecasting and portfolio selection based on ARX, grey system and RS theories”, Expert Systems with Application, Vol. 36 No. 3, pp. 5387-5392.

Kazemi, A., Moddarres, M., Mehregan, M.R. and Foruqi-Asl, A. (2010), “The forecast of transport sector energy demand by the Grey Markov Chain Model”, Conference on Energy Efficiency.

Khajavi, S., Najafi, Z. and Zinedine Zadeh, S. (2012), “Applying the grey models and the development of a simple way to forecast free cash flow of listed companies in Tehran stock exchange”, Journal of Financial and Management Engineering Exchange, Vol. 13, pp. 21-34.

Kothari, S.P. and Wasley, C.E. (1989), “Measuring security price performance in size-clustered samples”, The Accounting Review, Vol. 64 No. 2, pp. 228-249.

Liu, S. and Lin, Y. (2006), Grey Information, Springer, London.

Mashayekhi, B., Fadaee Nejad, M. and Kalateh Rahmani, R. (2009), “Explanatory power of accruals (abnormal) stock returns in relation to behavior: Effects of corporate profits and the systematic risk (β)”, Journal of Accounting and Auditing, Vol. 4, pp. 1-20.

Mohammadi, A. and Zeinodin Zade, S. (2011), “Appling grey forecasting method to forecast the portfolio’s rate of return in stock market of Iran”, Australian Journal of Business and Management Research, Vol. 1 No. 7, pp. 1-16.

Namazi, M. and Kiamehr, M. (2008), “Forecasting daily stock returns of listed companies in Tehran stock exchange using artificial neural networks”, Journal of Financial Research, Vol. 6 No. 3, pp. 60-72.

Pindyck, R. (1984), “Risk, inflation, and the stock market”, American Accounting Review, Vol. 74 No. 3, pp. 335-351.

Ping, Y. and Yang, H. (2004), “Using hybrid grey model to achieve revenue assurance of telecommunication companies”, Journal of Grey System, Vol. 7, pp. 39-50.

Pullets, J.M. and Wilson, M. (2010), “Average correlation and stock market returns”, Journal of Financial Economics, Vol. 96 No. 3, pp. 364-380.

Raei, R. and Chavoshi, K. (2003), “Forecasting of stock return in Tehran stock exchange: artificial neural networks and multi factors models”, J. Financial Study, Vol. 15 No. 5, pp. 97-120.

Verchenco, O. (2002), “Determinants of stock market volatility dynamics”, Working Paper, HEC University of Lausann.

Wang, C.-H. and Hsu, L. (2008), “Using genetic algorithms grey theory to forecast high technology industrial output”, Application Mathematics and Computation, Vol. 195 No. 1, pp. 256-263.

Wang, Z. (2013), “An optimized Nash nonlinear grey Bernoulli model for forecasting the main economic indices of high technology enterprises in China”, Computers & Industrial Engineering, Vol. 64 No. 0, pp. 780-787.

Zinedine Zadeh, S. (2011), “Predicting stock returns in Tehran Stock Exchange by using the Grey prediction model”, MA thesis, Faculty of Economics, Management and Social Sciences, Shiraz University.




How to Cite

Doryab, B. ., & Salehi, M. . (2018). Modeling and forecasting abnormal stock returns using the nonlinear Grey Bernoulli model. Journal of Economics, Finance and Administrative Science, 23(44), 95–112. Retrieved from