پیش بینی شاخص کل بورس اوراق بهادار تهران با استفاده از مدل شبکه عصبی نارکس (مقاله علمی وزارت علوم)
درجه علمی: نشریه علمی (وزارت علوم)
آرشیو
چکیده
این پژوهش با هدف تعیین تنظیمات بهینه مدل شبکه عصبی خودرگرسیون غیرخطی با ورودی های برون زا (نارکس) برای پیش بینی روز آتی شاخص کل بورس اوراق بهادار تهران انجام شده است. سایر اهداف شامل مقایسه عملکرد مدل نارکس با مدل های شبکه عصبی خودرگرسیون غیرخطی (نار) و ورودی - خروجی غیرخطی (نایو)، توسعه بازه زمانی پیش بینی با استفاده از شبکه عصبی نار، اعتبارسنجی مدل نارکس ازطریق تحلیل حساسیت و مقایسه عملکرد آن با مدل میانگین متحرک خودرگرسیون انباشته (آریما) است. طبق داده های شاخص کل از سال ۱۳۸۸ تا ۱۴۰۲، مدل نارکس برای پیش بینی روز آتی و مدل نار برای توسعه بازه زمانی پیش بینی به کار گرفته شد. عملکرد مدل نارکس با مدل های نار، نایو و آریما براساس درصد خطای مطلق مقایسه شد. برای تعیین تنظیمات بهینه مدل نارکس و مقایسه عملکرد مدل نار با آریما نیز میانگین مجذور خطا ملاک قرار گرفت. یافته ها نشان می دهد که مدل نارکس پیشنهادی، در ترکیب با داده های قیمت باز، بسته، سقف و کف، حجم معاملات و میانگین های متحرک ساده و نمایی بهترین عملکرد پیش بینی را داشته است. در مقایسه با سایر الگوریتم های آموزشی، الگوریتم لونبرگ - مارکوارت بالاترین دقت را ایجاد کرده است. نتایج اعتبارسنجی نیز برتری مدل نارکس را به الگوریتم های شبکه عصبی نار و نایو و مدل سنتی آریما تأیید می کند. این پژوهش نخستین بررسی از عملکرد شبکه عصبی نارکس در پیش بینی شاخص کل بورس تهران است و یافته های آن، علاوه بر توسعه دانش نظری در زمینه کاربرد شبکه عصبی پویا می تواند به عنوان ابزاری اثربخش در اختیار تحلیلگران بازار سرمایه قرار گیرد.Forecasting the Tehran Stock Exchange Dividend and Price Index (TEDPIX) Using a NARX Neural Network Model
This study aims to optimize the settings of the nonlinear autoregressive network with exogenous inputs (NARX) model for predicting the next-day Tehran Exchange Dividend and Price Index (TEDPIX), compare its performance with the nonlinear autoregressive (NAR) and nonlinear input-output (NIO) models, extend the prediction horizon using the NAR model, and validate the NARX model through sensitivity analysis and performance comparison with the traditional autoregressive integrated moving average (ARIMA) model. This study uses TEDPIX data from 2009 to 2023. The NARX model was employed to predict the next day's index, and the NAR model was used to extend the forecasting horizon. The performance of the NARX model was compared to the NAR, NIO, and ARIMA models, using the percentage of absolute error as the evaluation metric. The mean squared error was used to determine the optimal settings for the NARX model and compare the performance of the NAR model with ARIMA. The findings indicate that the proposed NARX model, when combined with open, close, high, and low prices, trading volume, simple moving average, and exponential moving average, delivers the best prediction performance. Additionally, the Levenberg-Marquardt training algorithm achieves the highest accuracy. The model validation results confirm the superiority of the NARX algorithm over the NAR and NIO models and the traditional ARIMA model. Keywords: NARX Neural Network, Machine Learning, Price Prediction, Stock Index JEL Codes: C45, C53, G12, G17 Introduction With the advancement of computational technologies and the growth of electronic trading, capital markets have expanded considerably, generating large volumes of financial data (Zeng et al., 2025). Analyzing this data is vital for improved decision-making and effective risk management (Rashid & Ismail, 2024). In Iran, the Tehran Exchange Dividend and Price Index (TEDPIX) is a key economic indicator, yet accurately forecasting its movements remains a challenge for market analysts (Chavoshi et al., 2022). Due to its nonlinear and dynamic nature (Osoolian et al., 2025), advanced techniques such as artificial neural networks have been proposed to enhance forecasting performance (Rafi et al., 2023). Traditional models like ARIMA (Autoregressive Integrated Moving Average) often fall short in volatile environments (Dhafer et al., 2022), whereas neural networks are better equipped to capture complex, nonlinear patterns (Shariffar et al., 2023). Among artificial neural network models, the Nonlinear Autoregressive model with eXogenous inputs (NARX) demonstrates higher accuracy in time series forecasting by considering the relationship between exogenous inputs and the target variable (Alcalde et al., 2024). It also exhibits greater efficiency by converging more rapidly to optimal weights (Jaiswal et al., 2025). Despite its advantages, the NARX model has not yet been applied to forecast TEDPIX specifically. This study develops a NARX-based forecasting model for TEDPIX, compares its performance with the NAR (Nonlinear Autoregressive) and NIO (Nonlinear Input-Output) models, evaluates different forecasting horizons, conducts sensitivity analysis, and benchmarks its results against ARIMA. The central question is whether NARX can provide more accurate forecasts for TEDPIX. Materials & Methods This study utilizes TEDPIX data from 2009 to 2023, obtained from the official website of the Tehran Securities Technology Management Company. The NARX model is employed to forecast the next day's index value, while the NAR model extends the prediction to longer horizons. The research follows a four-stage methodology: data collection and preparation, preprocessing, model configuration and execution, and performance evaluation. In addition to price and trading volume, several technical indicators—including Simple Moving Average (SMA), Exponential Moving Average (EMA), Moving Average Convergence Divergence (MACD), and Relative Strength Index (RSI)—were computed to define the model's input variables. During model configuration, the optimal number of neurons, the best input combinations, and the most effective training algorithm were identified. Model optimization was guided by the Mean Squared Error (MSE), while the Mean Absolute Error (MAE) was used to compare prediction accuracy across models. Following model execution, a sensitivity analysis was conducted to evaluate the impact of neuron count on forecasting accuracy. Finally, the predictive performance of the NARX model was benchmarked against the NAR, NIO, and ARIMA models to assess its relative forecasting effectiveness. Findings The results indicate that the optimal input set for the NARX model includes opening, closing, highest, and lowest prices, trading volume, SMA (10), EMA (10), SMA (50), and EMA (50). The model showed its best performance when the number of neurons was set according to the formulation proposed by Dhafer et al. (2022). Among training algorithms, Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient produced the most accurate outcomes, respectively. Model validation through sensitivity analysis confirmed its robustness: as shown in Figure 4, changes in the number of neurons resulted in controlled variations in accuracy, indicating model stability. Figure (4) Sensitivity analysis of the NARX model to the number of neurons Furthermore, a one-day-ahead forecasting comparison between NARX and ARIMA indicated the superior predictive capability of the proposed model. Over a 15-year period, the absolute percentage error for NARX was 0.32, compared to 0.55 for ARIMA (see Table 6). Table (6) Comparison results of the ARIMA model with the NARX model Time Horizon Forecasted Value (NARX) Forecasted Value (ARIMA) MAE – NARX (%) MAE – ARIMA (%) 15 Years 1,412,700 1,415,891 0.32 0.55 10 Years 1,414,200 1,416,041 0.43 0.56 5 Years 1,414,100 1,416,497 0.42 0.59 3 Years 1,413,300 1,416,040 0.36 0.56 Discussion and Conclusion To enhance TEDPIX forecasting accuracy, this study proposes a model based on the optimized design and configuration of the NARX network, achieving a notably low error rate of 0.00052. Addressing the second objective, the NARX model was benchmarked against its predecessors—NIO and NAR—demonstrating superior performance consistent with findings by Alcalde et al. (2024). Moreover, by leveraging the predictive capacity of the NAR model, the forecasting horizon was extended to 21 days. Sensitivity analysis regarding the number of neurons, aligned with the study's fourth objective, confirmed the model's robustness. Additionally, a performance comparison with the ARIMA model showed that NARX outperformed ARIMA, in line with previous research by Alshater et al. (2022), Devyatkin and Otmakhova (2021), and Badshah et al. (2023). Despite these contributions, the study faces several limitations, including a constrained time frame, reliance solely on price and technical indicators, sensitivity to model configuration, and limited generalizability to other contexts. Future research may improve model performance by developing more efficient training algorithms, integrating hybrid approaches, expanding applications to diverse markets, and optimizing the network architecture.
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