Modeling Uncertainty in Stock Price Indices Using a Hybrid NARX-Based Machine Learning Framework

Shafqat Iqbal (), Shakeel Ahmad, Xingfa Zhang (), Xiufeng Liu () and Sajawal Piracha
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Shafqat Iqbal: Masaryk University, Faculty of Economics and Administration
Shakeel Ahmad: Guangzhou University, School of Economics and Statistics
Xingfa Zhang: Guangzhou University, School of Economics and Statistics
Xiufeng Liu: Technical University of Denmark, Department of Technology, Management and Economics
Sajawal Piracha: Shanxi University of Finance and Economics, Department of Finance

A chapter in Innovations in Finance, 2026, pp 131-143 from Springer

Abstract: Abstract Financial market forecasting is vital for investors and financial institutions, yet it remains challenging due to the inherent complexity, nonlinearity, and uncertainty of stock market dynamics. This chapter introduces Fuzzy-NARX (FNARX), a novel hybrid model for stock market index forecasting. The model is distinguished by its data-driven fuzzy input generation, which employs Fuzzy C-Means (FCM) clustering to optimize interval partitioning. FNARX integrates fuzzy logic for data representation with Nonlinear Autoregressive with Exogenous Inputs (NARX) neural networks for time series forecasting. Historical stock market data are transformed into informative fuzzy input features using FCM clustering, Generalized Triangular Fuzzy Numbers (GTFNs), and Gaussian membership functions, capturing membership degrees in fuzzy sets defined over optimized intervals. These fuzzy inputs, which effectively represent market vagueness and uncertainty, are then processed by the NARX network. Empirical results on the Taiwan Stock Exchange (TAIEX) index dataset show that FNARX consistently outperforms benchmark models, including traditional fuzzy time series approaches, ARIMA, and a standard NARX model without fuzzy input. Residual analysis further validates the model’s adequacy and demonstrates the benefits of combining fuzzy logic with data-driven input representation and NARX networks, offering a valuable tool for improving portfolio management and investment decisions.

Keywords: Fuzzy-NARX (FNARX); Stock Market Forecasting; Neural Networks; Fuzzy Theory; Time Series (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-19314-8_13

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