[Paper Review] Neural networks for stock price prediction

Yuegang Song, Yulong Zhou+1 more|arXiv (Cornell University)|May 29, 2018

Stock Market Forecasting Methods18 references3 citations

TL;DR

This study evaluates five neural network models—back propagation (BP), radial basis function (RBF), general regression neural network (GRNN), support vector machine regression (SVMR), and least squares SVM regression (LS-SVMR)—for stock price prediction on three Chinese stocks (Bank of China, Vanke A, Kweichou Moutai). Using mean squared error (MSE) and mean absolute percentage error (MAPE) as metrics, BP neural networks consistently outperform the other four models across all stocks, demonstrating superior predictive accuracy and stability.

ABSTRACT

Due to the extremely volatile nature of financial markets, it is commonly accepted that stock price prediction is a task full of challenge. However in order to make profits or understand the essence of equity market, numerous market participants or researchers try to forecast stock price using various statistical, econometric or even neural network models. In this work, we survey and compare the predictive power of five neural network models, namely, back propagation (BP) neural network, radial basis function (RBF) neural network, general regression neural network (GRNN), support vector machine regression (SVMR), least squares support vector machine regresssion (LS-SVMR). We apply the five models to make price prediction of three individual stocks, namely, Bank of China, Vanke A and Kweichou Moutai. Adopting mean square error and average absolute percentage error as criteria, we find BP neural network consistently and robustly outperforms the other four models.

Motivation & Objective

• To evaluate and compare the predictive performance of five neural network models—BP, RBF, GRNN, SVMR, and LS-SVMR—in forecasting individual stock prices.
• To determine which model offers the highest accuracy and stability in predicting stock prices across different market conditions.
• To investigate whether the superior performance of BP neural networks is due to inherent structural advantages or kernel function choices.
• To test the hypothesis of market efficiency by analyzing prediction residuals and identifying systematic biases in forecast errors.

Proposed method

• Five neural network models were trained and tested on historical daily closing prices of three A-share stocks: Bank of China, Vanke A, and Kweichou Moutai.
• The back propagation (BP) neural network used a multilayer feedforward architecture with error backpropagation for weight adjustment.
• The radial basis function (RBF) network employed a single hidden layer with Gaussian radial basis functions for nonlinear mapping.
• General regression neural network (GRNN) used a nonparametric kernel-based approach for regression, relying on Parzen window estimation.
• Support vector machine regression (SVMR) and least squares SVM regression (LS-SVMR) applied structural risk minimization to solve convex quadratic programming problems for global optimization.
• Model performance was evaluated using mean squared error (MSE) and mean absolute percentage error (MAPE), with 100 independent runs to assess BP stability.

Experimental results

Research questions

• RQ1 Which of the five neural network models—BP, RBF, GRNN, SVMR, or LS-SVMR—delivers the most accurate stock price predictions across multiple stocks?
• RQ2 Does the BP neural network maintain consistent superiority over other models in terms of both accuracy and stability across different stocks and evaluation metrics?
• RQ3 How do different kernel functions (linear, polynomial, sigmoid, RBF) in SVMR affect prediction performance, and does the default RBF kernel yield optimal results?
• RQ4 Is the observed prediction bias in residuals consistent with market efficiency, or does it indicate exploitable inefficiencies in the stock price process?
• RQ5 Can the stability of the BP neural network be empirically verified through repeated training runs with random weight initialization?

Key findings

• The BP neural network achieved the lowest mean squared error (MSE) and mean absolute percentage error (MAPE) across all three stocks, outperforming RBF, GRNN, SVMR, and LS-SVMR consistently.
• For Bank of China, BP achieved an MSE of 0.009 and MAPE of 0.019, significantly lower than RBF (MSE: 0.010, MAPE: 0.020) and SVMR with RBF kernel (MSE: 0.012, MAPE: 0.023).
• On Vanke A, BP recorded an MSE of 2.976 and MAPE of 0.049, outperforming RBF (MSE: 4.686, MAPE: 0.065) and LS-SVMR (MSE: 5.472, MAPE: 0.072).
• For Kweichou Moutai, BP achieved an MSE of 395.1 and MAPE of 0.026, outperforming GRNN (MSE: 1103.6, MAPE: 0.048) and LS-SVMR (MSE: 405.5, MAPE: 0.027).
• The standard deviation of BP predictions across 100 runs was extremely low (e.g., 4.8×10⁻⁵ for MSE on Bank of China), confirming high stability despite random weight initialization.
• Residual analysis revealed a systematic negative bias (mean error eₜ < 0), contradicting market efficiency and indicating predictable patterns in price movements.