Document Type : Journal of Mathematics and Modeling in Finance (JMMF)
Authors
Department of Statistics and Informatics, University of Mosul, Mosul, Iraq
10.22054/jmmf.2026.90440.1248
Abstract
Stock price forecasting poses significant challenges due to non-stationarity, nonlinearity, and noise in financial markets, particularly for the Iraqi stock exchange. This study proposes an enhanced interval-valued forecasting model for daily prices of the Al Mansour Pharmaceutical Industries (MPI) company (2020–2025) using v-support vector regression (VSVR) with hyperparameters optimized via the waterwheel plant algorithm (WWPOA). The WWPOA approach tunes key VSVR parameters through population-based exploration and exploitation phases inspired by WWPOA, outperforming grid search (GS-VSVR) and cross-validation (CV-VSVR). Forecasting performance is evaluated using four criteria, namely mean absolute error , root mean squared error , direction accuracy and coefficient of determination . The empirical results show that the proposed model achieves lower values, compared to and indicating superior accuracy, robustness, and directional forecasting capability. On training data (637 days), WWPOA-VSVR achieves superior metrics for center and radius compared to baselines; testing results (308 days) confirm robustness. Further, Diebold-Mariano tests validate center-based WWPOA-VSVR superiority over radius-based at 95% confidence (p<0.05). On the training set, the center based WWPOA VSVR achieves MAE of about 0.18, RMSE of about 0.28, DA around 0.63, and R^2close to 0.93, while the radius based model attains MAE near 0.19, RMSE around 0.29, DA about 0.61, and R^2near 0.92. On the test set, center forecasts retain strong performance, with MAE around 0.20, RMSE about 0.30, DA near 0.60, and R^2approximately 0.92, and radius forecasts achieve MAE close to 0.17, RMSE near 0.27, DA about 0.57, and R^2around 0.88.
Keywords
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[2] W. Zhu, W. Dai, C. Tang, G. Zhou, Z. Liu and Y. Zhao, PMANet: a time series forecasting
model for Chinese stock price prediction, Scientific Reports, 14 (2024), pp. 18351.
[3] T. T. Thach, Forecasting Stock Market Indices Using Integration of Encoder, Decoder, and Attention Mechanism, Entropy, 27 (2025).
[4] A. D. Kayit and M. T. Ismail, Advancing stock price prediction through the development of hybrid ensembles: a comprehensive comparative analysis of machine learning approaches, Journal of Big Data, 12 (2025).
[5] P. H. Vuong et al., A bibliometric literature review of stock price forecasting: From
statistical model to deep learning approach, Science Progress, 107 (2024).
[6] Q. Ge, Enhancing stock market forecasting: A hybrid model for accurate prediction of S&P 500 and CSI 300 future prices, Expert Systems with Applications, 260 (2025), pp. 125380.
[7] H. Mehtarizadeh et al., Stock price prediction with SCA-LSTM network and statistical
model ARIMA-GARCH, The Journal of Supercomputing, 81 (2025).
[8] S. S. Bagalkot et al., Novel grey wolf optimizer based parameters selection for GARCH
and ARIMA models for stock price prediction, PeerJ Computer Science, 10 (2024), pp. e1735.
[9] J. K. Mutinda and A. K. Langat, Stock price prediction using combined GARCH-AI models,
Scientific African, 26 (2024).
[10] T. B. Shahi et al., Stock Price Forecasting with Deep Learning: A Comparative Study,
Mathematics, 8 (2020).
[11] C.-Y. Yang et al., Advancing Financial Forecasts: Stock Price Prediction Based on Time
Series and Machine Learning Techniques, Applied Artificial Intelligence, 38 (2024).
[12] B. M. Henrique, V. A. Sobreiro and H. Kimura, Stock price prediction using support
vector regression on daily and up to the minute prices, The Journal of Finance and Data Science, 4 (2018), pp. 183–201.
[13] A. Mahmoodi et al., A developed stock price forecasting model using support vector machine combined with metaheuristic algorithms, Opsearch, 60 (2023), pp. 59–86.
[14] R. Kuo and T.-H. Chiu, Hybrid of jellyfish and particle swarm optimization algorithm-based support vector machine for stock market trend prediction, Applied Soft Computing, 154 (2024), pp. 111394.
[15] M. Qasim, Z. Algamal and H. M. Ali, A binary QSAR model for classifying neuraminidase inhibitors of influenza A viruses (H1N1) using the combined minimum redundancy maximum relevancy criterion with the sparse support vector machine, SAR and QSAR in Environmental Research, 29 (2018), pp. 517–527.
[16] A. Staffini, Stock price forecasting by a deep convolutional generative adversarial network, Frontiers in Artificial Intelligence, 5 (2022), pp. 837596.
[17] T. Kim and H. Y. Kim, Forecasting stock prices with a feature fusion LSTM-CNN model
using different representations of the same data, PLoS One, 14 (2019), pp. e0212320.
[18] M. Nikou et al., Stock price prediction using deep learning algorithm and its comparison with machine learning algorithms, Intelligent Systems in Accounting, Finance and Management, 26 (2019), pp. 164–174.
[19] A. W. Li and G. S. Bastos, Stock market forecasting using deep learning and technical
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[20] S. Mukherjee et al., Stock market prediction using deep learning algorithms, CAAI Trans
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[25] O. M. Ismael et al., Improving Parameters of V-Support Vector Regression with Feature
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estimation and feature selection in v-support vector regression based on opposition-based
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[29] T. Xiong et al., Multiple-output support vector regression with a firefly algorithm for
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[32] V. N. Vapnik, An overview of statistical learning theory, IEEE Transactions on Neural
Networks, 10 (1999), pp. 988–999.
[33] P. Y. Hao, Pair-ν-SVR: A Novel and Efficient Pairing nu-Support Vector Regression
Algorithm, IEEE Transactions on Neural Networks and Learning Systems, 28 (2017), pp.
2503–2515.
[34] D. Kong et al., Tool wear monitoring based on kernel principal component analysis and
v-support vector regression, International Journal of Advanced Manufacturing Technology, 89 (2016), pp. 175–190.
[35] N. Li et al., Force-based tool condition monitoring for turning process using v-support
vector regression, International Journal of Advanced Manufacturing Technology, 91 (2016),
pp. 351–361.
[36] Y. Liu and G. Pender, A flood inundation modelling using v-support vector machine
regression model, Engineering Applications of Artificial Intelligence, 46 (2015), pp. 223–231.
[37] X. Teng et al., Adaptive feature selection using v-shaped binary particle swarm optimization, PLoS One, 12 (2017), pp. e0173907.
[38] Y. Zhang and Y. Xie, Forecasting of short-term freeway volume with v-support vector
machines, Transportation Research Record, 2024 (2007), pp. 92–99.
[39] P. Tsirikoglou et al., A hyperparameters selection technique for support vector regression models, Applied Soft Computing, 61 (2017), pp. 139–148.
[40] J.-S. Chou and A.-D. Pham, Nature-inspired metaheuristic optimization in least squares
support vector regression for obtaining bridge scour information, Information Sciences, 399
(2017), pp. 64–80.
[41] R. Laref et al., On the optimization of the support vector machine regression hyperparameters setting for gas sensors array applications, Chemometrics and Intelligent Laboratory Systems, 184 (2019), pp. 22–27.
[42] S. Li et al., Parameter optimization of support vector regression based on sine cosine
algorithm, Expert Systems with Applications, 91 (2018), pp. 63–77.
[43] V. Cherkassky and Y. Ma, Practical selection of SVM parameters and noise estimation
for SVM regression, Neural Networks, 17 (2004), pp. 113–126.
[44] K. Ito and R. Nakano, Optimizing support vector regression hyperparameters based on
cross-validation, Proceedings of the International Joint Conference on Neural Networks,
(2003), pp. 2077–2082.
[45] C.-H. Wu et al., A novel hybrid genetic algorithm for kernel function and parameter
optimization in support vector regression, Expert Systems with Applications, 36 (2009), pp.
4725–4735.
[46] M. N. Amar and N. Zeraibi, Application of hybrid support vector regression artificial bee
colony for prediction of MMP in CO2-EOR process, Petroleum, (2018).
[47] C.-F. Huang, A hybrid stock selection model using genetic algorithms and support vector regression, Applied Soft Computing, 12 (2012), pp. 807–818.
[48] C.-T. Cheng et al., Optimizing hydropower reservoir operation using hybrid genetic algo
rithm and chaos, Water Resources Management, 22 (2007), pp. 895–909.
[49] W.-C. Hong et al., SVR with hybrid chaotic genetic algorithms for tourism demand forecasting, Applied Soft Computing, 11 (2011), pp. 1881–1890.
[50] J. Cheng et al., Adaptive chaotic cultural algorithm for hyperparameters selection of support vector regression, International Conference on Intelligent Computing, (2009), pp. 286–293.
[51] B. ¨ Ust¨ un et al., Determination of optimal support vector regression parameters by genetic algorithms and simplex optimization, Analytica Chimica Acta, 544 (2005), pp. 292 -305.
[52] J. Zhang et al., Optimization enhanced genetic algorithm-support vector regression for the prediction of compound retention indices in gas chromatography, Neurocomputing, 240 (2017), pp. 183–190.
[53] G. Cao and L. Wu, Support vector regression with fruit fly optimization algorithm for seasonal electricity consumption forecasting, Energy, 115 (2016), pp. 734–745.
[54] E. Abdulsaed et al., Hyperparameter optimization for convolutional neural networks using the salp swarm algorithm, Informatica, 47 (2023).
[55] Z. Y. Algamal et al., Improving grasshopper optimization algorithm for hyperparameters estimation and feature selection in support vector regression, Chemometrics and Intelligent Laboratory Systems, 208 (2021), pp. 104196.
[56] A. A. Abdelhamid et al., Waterwheel plant algorithm: a novel metaheuristic optimization method, Processes, 11 (2023), pp. 1502.
[57] A. A. Alhussan et al., A binary waterwheel plant optimization algorithm for feature selection, IEEE Access, 11 (2023), pp. 94227–94251.
[58] H. Zhang et al., Forecasting monthly copper price: A comparative study of various machine learning-based methods, Resources Policy, 73 (2021).
[59] X. Li et al., Forecasting the lithium mineral resources prices in China: Evidence with Facebook Prophet (Fb-P) and Artificial Neural Networks (ANN) methods, Resources Policy, 82 (2023), pp. 103580.
[60] F. X. Diebold and R. S. Mariano, Comparing predictive accuracy, Journal of Business and Economic Statistics, 13 (1995), pp. 253–263.
Traditional Predictive Models to Large Language Models, Computational Economics, (2025).
[2] W. Zhu, W. Dai, C. Tang, G. Zhou, Z. Liu and Y. Zhao, PMANet: a time series forecasting
model for Chinese stock price prediction, Scientific Reports, 14 (2024), pp. 18351.
[3] T. T. Thach, Forecasting Stock Market Indices Using Integration of Encoder, Decoder, and Attention Mechanism, Entropy, 27 (2025).
[4] A. D. Kayit and M. T. Ismail, Advancing stock price prediction through the development of hybrid ensembles: a comprehensive comparative analysis of machine learning approaches, Journal of Big Data, 12 (2025).
[5] P. H. Vuong et al., A bibliometric literature review of stock price forecasting: From
statistical model to deep learning approach, Science Progress, 107 (2024).
[6] Q. Ge, Enhancing stock market forecasting: A hybrid model for accurate prediction of S&P 500 and CSI 300 future prices, Expert Systems with Applications, 260 (2025), pp. 125380.
[7] H. Mehtarizadeh et al., Stock price prediction with SCA-LSTM network and statistical
model ARIMA-GARCH, The Journal of Supercomputing, 81 (2025).
[8] S. S. Bagalkot et al., Novel grey wolf optimizer based parameters selection for GARCH
and ARIMA models for stock price prediction, PeerJ Computer Science, 10 (2024), pp. e1735.
[9] J. K. Mutinda and A. K. Langat, Stock price prediction using combined GARCH-AI models,
Scientific African, 26 (2024).
[10] T. B. Shahi et al., Stock Price Forecasting with Deep Learning: A Comparative Study,
Mathematics, 8 (2020).
[11] C.-Y. Yang et al., Advancing Financial Forecasts: Stock Price Prediction Based on Time
Series and Machine Learning Techniques, Applied Artificial Intelligence, 38 (2024).
[12] B. M. Henrique, V. A. Sobreiro and H. Kimura, Stock price prediction using support
vector regression on daily and up to the minute prices, The Journal of Finance and Data Science, 4 (2018), pp. 183–201.
[13] A. Mahmoodi et al., A developed stock price forecasting model using support vector machine combined with metaheuristic algorithms, Opsearch, 60 (2023), pp. 59–86.
[14] R. Kuo and T.-H. Chiu, Hybrid of jellyfish and particle swarm optimization algorithm-based support vector machine for stock market trend prediction, Applied Soft Computing, 154 (2024), pp. 111394.
[15] M. Qasim, Z. Algamal and H. M. Ali, A binary QSAR model for classifying neuraminidase inhibitors of influenza A viruses (H1N1) using the combined minimum redundancy maximum relevancy criterion with the sparse support vector machine, SAR and QSAR in Environmental Research, 29 (2018), pp. 517–527.
[16] A. Staffini, Stock price forecasting by a deep convolutional generative adversarial network, Frontiers in Artificial Intelligence, 5 (2022), pp. 837596.
[17] T. Kim and H. Y. Kim, Forecasting stock prices with a feature fusion LSTM-CNN model
using different representations of the same data, PLoS One, 14 (2019), pp. e0212320.
[18] M. Nikou et al., Stock price prediction using deep learning algorithm and its comparison with machine learning algorithms, Intelligent Systems in Accounting, Finance and Management, 26 (2019), pp. 164–174.
[19] A. W. Li and G. S. Bastos, Stock market forecasting using deep learning and technical
analysis: a systematic review, IEEE Access, 8 (2020), pp. 185232–185242.
[20] S. Mukherjee et al., Stock market prediction using deep learning algorithms, CAAI Trans
actions on Intelligence Technology, 8 (2023), pp. 82–94.
[21] A. L. S. Maia et al., Forecasting models for interval-valued time series, Neurocomputing,
71 (2008), pp. 3344–3352.
[22] Q. Lu et al., Forecasting interval-valued crude oil prices using asymmetric interval models, Quantitative Finance, 22 (2022), pp. 2047–2061.
[23] J. Wang et al., An enhanced interval-valued decomposition integration model for stock price prediction based on comprehensive feature extraction and optimized deep learning, Expert Systems with Applications, 243 (2024).
[24] D. Wang et al., Interval-valued financial time series prediction based on improved Elman neural network, ICIC Express Letters, 13 (2019), pp. 159–166.
[25] O. M. Ismael et al., Improving Parameters of V-Support Vector Regression with Feature
Selection in Parallel by Using Quasi-Oppositional and Harris Hawks Optimization Algorithm,
Informatyka, 14 (2024), pp. 113–118.
[26] O. M. Ismael et al., Improving Harris hawks optimization algorithm for hyperparameters
estimation and feature selection in v-support vector regression based on opposition-based
learning, Journal of Chemometrics, 34 (2020).
[27] O. M. Ismael et al., A new adaptive algorithm for v-support vector regression with feature selection using Harris hawks optimization algorithm, Journal of Physics: Conference Series, 1897 (2021), pp. 012057.
[28] J. Wang et al., Improved v-support vector regression model based on variable selection and brain storm optimization for stock price forecasting, Applied Soft Computing, 49 (2016), pp. 164–178.
[29] T. Xiong et al., Multiple-output support vector regression with a firefly algorithm for
interval-valued stock price index forecasting, Knowledge-Based Systems, 55 (2014), pp. 87
100.
[30] A. Kazem et al., Support vector regression with chaos-based firefly algorithm for stock
market price forecasting, Applied Soft Computing, 13 (2013), pp. 947–958.
[31] M. Jiang et al., A novel interval dual convolutional neural network method for interval
valued stock price prediction, Pattern Recognition, 145 (2024).
[32] V. N. Vapnik, An overview of statistical learning theory, IEEE Transactions on Neural
Networks, 10 (1999), pp. 988–999.
[33] P. Y. Hao, Pair-ν-SVR: A Novel and Efficient Pairing nu-Support Vector Regression
Algorithm, IEEE Transactions on Neural Networks and Learning Systems, 28 (2017), pp.
2503–2515.
[34] D. Kong et al., Tool wear monitoring based on kernel principal component analysis and
v-support vector regression, International Journal of Advanced Manufacturing Technology, 89 (2016), pp. 175–190.
[35] N. Li et al., Force-based tool condition monitoring for turning process using v-support
vector regression, International Journal of Advanced Manufacturing Technology, 91 (2016),
pp. 351–361.
[36] Y. Liu and G. Pender, A flood inundation modelling using v-support vector machine
regression model, Engineering Applications of Artificial Intelligence, 46 (2015), pp. 223–231.
[37] X. Teng et al., Adaptive feature selection using v-shaped binary particle swarm optimization, PLoS One, 12 (2017), pp. e0173907.
[38] Y. Zhang and Y. Xie, Forecasting of short-term freeway volume with v-support vector
machines, Transportation Research Record, 2024 (2007), pp. 92–99.
[39] P. Tsirikoglou et al., A hyperparameters selection technique for support vector regression models, Applied Soft Computing, 61 (2017), pp. 139–148.
[40] J.-S. Chou and A.-D. Pham, Nature-inspired metaheuristic optimization in least squares
support vector regression for obtaining bridge scour information, Information Sciences, 399
(2017), pp. 64–80.
[41] R. Laref et al., On the optimization of the support vector machine regression hyperparameters setting for gas sensors array applications, Chemometrics and Intelligent Laboratory Systems, 184 (2019), pp. 22–27.
[42] S. Li et al., Parameter optimization of support vector regression based on sine cosine
algorithm, Expert Systems with Applications, 91 (2018), pp. 63–77.
[43] V. Cherkassky and Y. Ma, Practical selection of SVM parameters and noise estimation
for SVM regression, Neural Networks, 17 (2004), pp. 113–126.
[44] K. Ito and R. Nakano, Optimizing support vector regression hyperparameters based on
cross-validation, Proceedings of the International Joint Conference on Neural Networks,
(2003), pp. 2077–2082.
[45] C.-H. Wu et al., A novel hybrid genetic algorithm for kernel function and parameter
optimization in support vector regression, Expert Systems with Applications, 36 (2009), pp.
4725–4735.
[46] M. N. Amar and N. Zeraibi, Application of hybrid support vector regression artificial bee
colony for prediction of MMP in CO2-EOR process, Petroleum, (2018).
[47] C.-F. Huang, A hybrid stock selection model using genetic algorithms and support vector regression, Applied Soft Computing, 12 (2012), pp. 807–818.
[48] C.-T. Cheng et al., Optimizing hydropower reservoir operation using hybrid genetic algo
rithm and chaos, Water Resources Management, 22 (2007), pp. 895–909.
[49] W.-C. Hong et al., SVR with hybrid chaotic genetic algorithms for tourism demand forecasting, Applied Soft Computing, 11 (2011), pp. 1881–1890.
[50] J. Cheng et al., Adaptive chaotic cultural algorithm for hyperparameters selection of support vector regression, International Conference on Intelligent Computing, (2009), pp. 286–293.
[51] B. ¨ Ust¨ un et al., Determination of optimal support vector regression parameters by genetic algorithms and simplex optimization, Analytica Chimica Acta, 544 (2005), pp. 292 -305.
[52] J. Zhang et al., Optimization enhanced genetic algorithm-support vector regression for the prediction of compound retention indices in gas chromatography, Neurocomputing, 240 (2017), pp. 183–190.
[53] G. Cao and L. Wu, Support vector regression with fruit fly optimization algorithm for seasonal electricity consumption forecasting, Energy, 115 (2016), pp. 734–745.
[54] E. Abdulsaed et al., Hyperparameter optimization for convolutional neural networks using the salp swarm algorithm, Informatica, 47 (2023).
[55] Z. Y. Algamal et al., Improving grasshopper optimization algorithm for hyperparameters estimation and feature selection in support vector regression, Chemometrics and Intelligent Laboratory Systems, 208 (2021), pp. 104196.
[56] A. A. Abdelhamid et al., Waterwheel plant algorithm: a novel metaheuristic optimization method, Processes, 11 (2023), pp. 1502.
[57] A. A. Alhussan et al., A binary waterwheel plant optimization algorithm for feature selection, IEEE Access, 11 (2023), pp. 94227–94251.
[58] H. Zhang et al., Forecasting monthly copper price: A comparative study of various machine learning-based methods, Resources Policy, 73 (2021).
[59] X. Li et al., Forecasting the lithium mineral resources prices in China: Evidence with Facebook Prophet (Fb-P) and Artificial Neural Networks (ANN) methods, Resources Policy, 82 (2023), pp. 103580.
[60] F. X. Diebold and R. S. Mariano, Comparing predictive accuracy, Journal of Business and Economic Statistics, 13 (1995), pp. 253–263.
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