Development of Financial Indicator Set for Automotive Stock Performance Prediction Using Adaptive Neuro-Fuzzy Inference System

Abstract

This study investigates the predictive performance of financial indicators in forecasting stock prices within the automotive sector using an adaptive neuro-fuzzy inference system (ANFIS). In light of the growing complexity of global financial markets and the increasing demand for automated, data-driven forecasting models, this research aims to identify those financial ratios that most accurately reflect price dynamics in this specific industry. The model incorporates four widely used financial indicators, return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM), as inputs. The analysis is based on real financial and market data from automotive companies, and model performance was assessed using RMSE, nRMSE, and confidence intervals. The results indicate that the full model, including all four indicators, achieved the highest accuracy and prediction stability, while the exclusion of ROA or ROE significantly deteriorated model performance. These findings challenge the weak-form efficiency hypothesis and underscore the relevance of firm-level fundamentals in stock price formation. This study’s sector-specific approach highlights the importance of tailoring predictive models to industry characteristics, offering implications for both financial modeling and investment strategies. Future research directions include expanding the indicator set, increasing the sample size, and testing the model across additional industry domains.

1. Introduction

In the context of 21st-century global financial markets, the development of automated trading systems and stock market forecasting models has become a central focus for both academic researchers and financial practitioners. Against this backdrop, the present study makes a distinct contribution by adopting an industry-specific, cross-market perspective centered on the automotive sector—an angle that has not been systematically explored in the extant literature. In an increasingly complex economic environment, investors seek to make rapid and well-founded decisions, which necessitates the support of highly reliable predictive models. While the existing literature offers numerous approaches to modeling, many of these solutions exhibit limited effectiveness or are tailored exclusively to specific exchanges or national economies. By contrast, our sector-level approach allows us to exploit the structural homogeneity of automotive manufacturers—shared supply chains, synchronized business cycles, and comparable regulatory regimes—to uncover clearer and statistically more robust links between firm-level fundamentals and equity prices. This fills a recognized gap in prior research, which rarely considers how intra-industry commonalities can sharpen the informational content of financial ratios.

One of the primary challenges in developing predictive models lies in the selection of appropriate input variables. Previous research highlights that portfolio decisions are significantly influenced by market volatility and investors’ risk tolerance, emphasizing the critical role of fundamental financial indicators in forecasting stock performance (Bányai et al., 2025). The identification of relevant fundamental indicators is crucial, as the accuracy of forecasts largely depends on the quality and relevance of the input data (Alsubaie et al., 2019). Moreover, the effective operation of artificial intelligence-based models requires the processing of vast datasets, which demands substantial computational power and energy consumption. As a result, only systems equipped with advanced technological infrastructure can deliver predictive performance at an acceptable standard, placing significant financial and logistical burdens on researchers (Sharma et al., 2025). A phenomenon frequently observed in the practical application of AI-based stock market algorithms but insufficiently addressed in the literature is the tendency of such systems to lose predictive efficacy over time. This degradation is often not traceable within the models themselves, which are generally unable to account for the underlying causes of reduced performance.

This issue may be partially mitigated through the incorporation of stable and domain-relevant fundamental indicators, which can enhance the long-term viability of predictive systems and mitigate the drift that plagues many black-box algorithms. The objective of this research is to develop a predictive model capable of forecasting stock prices for companies in the automotive sector, by identifying a set of reliable and industry-specific financial indicators to be used as input variables. This novel combination of an adaptive neuro-fuzzy inference system (ANFIS) with an explicitly sector-specific variable set represents, to the best of our knowledge, the first attempt to generalize fuzzy–neural forecasting beyond single-country or exchange-bound applications in the automotive domain. The choice of the automotive industry is justified by its substantial macroeconomic significance. Globally, the automotive industry was valued at approximately USD 4.7 trillion in 2022, contributing around 3% to the global GDP (ZipDo, 2025). Furthermore, it directly employed over 9 million individuals worldwide, representing more than 5% of global manufacturing employment, and indirectly supported an estimated total of over 50 million jobs globally (Oica, 2023; ZipDo, 2025). In terms of consumption, global automotive production surpassed 82 million vehicles in 2022, and in 2023 rebounded to approximately 90 million units, strongly influencing global consumption patterns (Automotive, 2024; ZipDo, 2025). Given these significant economic impacts, forecasting the future performance of the automotive sector is of crucial importance to investors and policymakers alike. Regularly adjusting the portfolio of long-term investors is an essential aspect, as portfolios age and investors experience a reduction in the dispersion of returns, while the risk differentials between different portfolios increase (Bányai et al., 2024). The automotive sector faces unique valuation challenges. Traditional valuation metrics often struggle to accurately reflect automakers’ substantial R&D expenditures and intangible assets; for instance, research by Ehie and Olibe (2010) demonstrated that even major automotive companies’ R&D spending and recognized intangible assets had little significant correlation with market values, highlighting gaps in conventional financial modeling (Ehie & Olibe, 2010). Moreover, the industry’s high capital intensity and cyclical volatility have historically resulted in low and unstable valuations. According to Helper and Henderson (2014), over 500 automotive manufacturers have ceased operations in the U.S. alone, and even industry leaders such as General Motors have faced bankruptcy, clearly illustrating how rapidly macroeconomic downturns can compromise automotive valuations (Helper & Henderson, 2014). Recent valuation extremes further underscore this issue: Tesla’s market capitalization surged dramatically from under USD 100 billion to more than USD 1 trillion within two years, substantially surpassing much larger incumbents, while established firms like Ford and Volkswagen experienced significant stock price increases solely upon announcing plans for electrification (Perkins & Murmann, 2018). These stark valuation discrepancies reinforce the motivation for developing a sector-specific and more robust forecasting model for automotive stock performance. The uniqueness of the proposed model lies in its industry-specific focus, which distinguishes it from traditional models that typically concentrate on country-specific or exchange-based analyses and rarely explore sector-level interdependencies. By demonstrating that a parsimonious set of automotive-relevant ratios can outperform broader, exchange-level benchmarks, this study provides methodological guidance for future research that seeks to tailor forecasting systems to other industries with comparable structural coherence. By applying a neuro-fuzzy inference system, this study aims to construct a set of indicators that offer predictive capabilities grounded in the financial fundamentals specific to the automotive industry. The neuro-fuzzy framework enables a more nuanced interpretation of complex, nonlinear relationships, thereby enhancing predictive accuracy and supporting direct applicability in algorithmic trading systems. Consequently, the proposed model not only seeks to improve forecasting precision for automotive firms but also provides a methodological foundation adaptable to other sector-level financial forecasting models. A rigorous analysis of stock performance and financial indicators in this domain has the potential to support investment decisions and strengthen investor confidence, thereby contributing to the sustainable development and growth of financial markets.

2. Literature Review

The stock exchange constitutes the principal institutional capillary of advanced market economies: it channels savings toward real-economic investment while providing a unified platform for the transparent allocation of risk. Owing to its organizational architecture, membership system, central clearing, and supervisory oversight, transactions in equity, bond, and derivative markets can be settled, repriced, and audited, thereby reducing contractual uncertainty (Rubóczky, 1999). In the price-formation process, the exchange acts as a decentralized information aggregator: heterogeneous, frequently asymmetric information held by market participants is synthesized in the order book as price signals, which subsequently serve as reference quotes for over-the-counter transactions as well (Gál, 2016). From a historical perspective, market development has proceeded in tandem with the expansion of commercial and communication infrastructures. Seventeenth-century Amsterdam equity trading still required spontaneous physical presence, whereas modern platforms such as NASDAQ are based entirely on electronic order-matching algorithms (Michie, 1997). These technological leaps significantly narrowed bid–ask spreads and deepened liquidity, yet they also accelerated the global transmission of market shocks. The systemic role of stock exchanges becomes most visible in crisis episodes: the self-reinforcing sell-off of the 1929 “Black Tuesday,” the confidence crisis triggered by the 2008 Lehman collapse, and the turbulence induced by the 2020 pandemic each demonstrated that dislocations in securities markets can swiftly generate real-economic recessions (Gjerstad & Smith, 2009; Muraközy, 2016).

2.1. Evolution of Trading Techniques and Analytical Approaches

Since the 2000s, the dominance of high-frequency trading (HFT) and programmed algorithms has introduced a new risk dimension: while micro-second decision cycles deepen liquidity, ultra-rapid position reshuffling can amplify both the speed and the amplitude of price dislocations (Hossain, 2022; Varga, 2021). Intensifying global capital flows further strengthen equity–FX interactions; Insaidoo et al. (2024) show that the rise in international portfolio investment has created a statistically significant link between cross-border capital movements and short-term exchange-rate volatility. Corporate valuation and market pricing are explored through two foundational paradigms, fundamental and technical analysis, each resting on distinct premises yet jointly integral to contemporary portfolio management. Fundamental analysis posits that a share’s intrinsic value equals the present value of the firm’s future cash flows, which can be quantified through a coordinated examination of financial statements, corporate-governance quality, and the macroeconomic environment (Prohaska et al., 2011). The methodology distinguishes several hierarchical levels. At the macro level, GDP growth, inflation, and interest rates determine capital flows and the cost of capital (Kandi et al., 2023). At the industry level, entry barriers, regulatory regimes, and competitive intensity, often analyzed via Porter’s Five Forces, shape profitability prospects (Silpa et al., 2017). At the firm level, liquidity, profitability, efficiency, and leverage ratios, typically ROA, ROE, P/E, and DER, function as quantitative imprints of managerial performance (Ajha et al., 2024). The chief strength of the approach lies in its long-term investment horizon and its capacity to detect under- or overvalued assets; its limitations include the under-modeling of short-term sentiment and behavioral biases, as well as considerable data and estimation uncertainty (Spritzer & Freitas, 2006).

Technical analysis treats price and volume time series as carriers of all pertinent information. Its tool-set rests on two pillars. First, a variety of indicators, RSI, Bollinger Bands, and moving-average convergence–divergence (MACD), quantify momentum, volatility, and trend strength (Lee et al., 2022; Vasantha et al., 2012). Second, pattern recognition such as head-and-shoulders, double tops, or triangles infers demand–supply dynamics (Nguyen et al., 2023; Tripathi et al., 2023). The method offers rapid market feedback and modest data requirements; however, visual interpretation is inherently subjective, and market noise may distort signals (Wiiava et al., 2022). To mitigate these constraints, modern technical analysis increasingly integrates machine learning and time-series forecasting algorithms: wavelet-filtered indicators, LSTM networks, and principal-component reduction have each demonstrated performance gains in short-term prediction (Bandara et al., 2015; Postolache et al., 2010).

2.2. Advances and Applications of Artificial Intelligence and Neuro-Fuzzy Systems

The classical fundamental–technical dichotomy has been augmented by the rapidly evolving toolkit of artificial intelligence (AI). AI-based models are suited to processing high-dimensional, nonlinear, and heteroskedastic financial data: they can compress structural market regularities into latent representations not explicitly specified a priori, thereby offering broader predictive performance than linear econometric frameworks (Buchanan, 2005; Cappello et al., 2023). Among the most promising avenues are deep neural networks, rule-based fuzzy systems, and their hybrid integrations.

Artificial neural networks (ANNs) are layered structures inspired by biological analogies; as universal function approximators with sufficient parameters and training data, they can represent complex nonlinear mappings. Feed-forward networks (FNNs) proved their approximation capability in early stock market models, yet the time-dependent patterns of financial series are captured more effectively by recurrent networks (RNNs) and their long short-term memory (LSTM) variants (Asif et al., 2021). The learning core is back-propagation gradient descent, iteratively refining parameters to minimize prediction error (Carbonnelle & De Vleeschouwer, 2019). To shield against noise and regime shifts, analysts routinely employ regularization techniques including dropout, L1/L2 penalties, and hybrid input transformations such as wavelet-filtered technical indicators or principal-component-reduced fundamental variables (Galimberti & Repetto, 2023). While such combinations have outperformed traditional ARIMA or GARCH schemes in many price- and volatility-forecasting tasks, they raise issues of interpretability, as the network’s internal representations are only partially transparent to financial decision-makers (Sloane & Silva, 2019). The demand for explainability has spawned post hoc methods such as SHAP values and layer-wise relevance propagation, yet their incorporation into investment practice remains nascent.

Zadeh’s fuzzy-set theory offers a multivalued logical framework for formalizing uncertain, linguistically defined rules, an advantage in fragmented and often opaque financial information environments (Tamir et al., 2015). Via membership functions, variables are characterized not binarily but on a 0–1 continuum, enabling partial truth-values for states such as “high volatility” or “low liquidity” (Bělohlávek et al., 2017). The inference process proceeds through fuzzification, rule application, aggregation, and defuzzification, collectively embedding qualitative market knowledge into quantitative models. Two fuzzy architectures dominate practice. The Mamdani system is more intuitive, as both rules and outputs remain fuzzy prior to defuzzification. By contrast, the Sugeno–Takagi–Kang (TSK) model relies on linear or constant inference kernels, rendering it numerically efficient and suitable for real-time trading applications, particularly with high-frequency data (Ontiveros-Robles et al., 2020).

The ANFIS merges the parameter-learning capacity of neural networks with the rule-based, interpretable structure of fuzzy logic (Duy & Van Cuong, 2014). The first layer fuzzifies inputs, whereas intermediate layers adaptively update the weights of Sugeno-type rules via a hybrid learning algorithm (least squares plus gradient descent) (Mosavi et al., 2021). Empirical evidence underscores the model’s predictive potential: with a carefully selected macro-variable and technical variable set, the ANFIS achieved 98.3% accuracy for the ISE 100 index’s monthly returns (Boyacioglu & Avci, 2010), and outperformed both back-propagation networks and ARIMA on the Dhaka Stock Exchange (Banik et al., 2012). Performance, however, is highly sensitive to feature selection; expanding the input dimension can trigger rule explosion and hamper interpretability. This challenge is mitigated through meta-heuristic optimizers, e.g., particle swarm optimization or the imperialist competitive algorithm, that automatically search for the most informative variable subset (Barak et al., 2015). Advantages and challenges: The neuro-fuzzy framework simultaneously addresses nonlinearity, uncertainty, and interpretability requirements, yet its price is heightened computational cost and reduced model transparency (Chen et al., 2016). Nonetheless, it ranks among the most versatile methodological directions in financial-market research, especially where integrated, adaptive processing of fundamental and technical information is indispensable.

The recent literature increasingly utilizes adaptive neuro-fuzzy inference systems (ANFISs) for forecasting stock prices based on fundamental financial indicators (Boyacioglu & Avci, 2010). For instance, Mohamed et al. (2021), analyzing data from 58 companies, revealed that among various corporate performance metrics such as return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM), ROE exhibited the strongest predictive power regarding stock prices, whereas ROA was the least influential. Additionally, EPS emerged as the most significant profitability indicator, while PM was found to be the least impactful (Mohamed et al., 2021). In addition to these profitability indicators, other financial metrics such as liquidity ratios have also been linked to stock price movements. For instance, Suryana and Anggadini (2020) observed that a higher current ratio is significantly associated with higher stock prices in retail-sector companies (Suryana & Anggadini, 2020). Moreover, recent findings by Suroso (2022) suggest that the debt-to-equity ratio may also serve as a viable predictor of stock market performance, as companies with higher leverage levels tend to experience lower stock returns, indicating its predictive relevance.

These findings align with previous research outcomes, such as those by Idawati and Wahyudi (2015), who demonstrated that EPS and ROA positively influence stock prices in Indonesian firms, thus justifying the need for further empirical validation of their relevance through expert interviews conducted in the present study.

To date, the literature has not sufficiently addressed sector-specific stock performance forecasting in the automotive industry, particularly through the exclusive use of fundamental financial indicators; this study fills this gap by focusing explicitly on feature selection and enhancing model interpretability in predicting automotive stock performance.

3. Materials and Methods

The research followed a sequential mixed-method design consisting of two primary phases: qualitative scoping and quantitative modeling. Initially, a comprehensive literature review was conducted to identify commonly used financial indicators relevant to predicting stock market performance. Specifically, we used the Google Scholar and Scopus databases to systematically identify relevant academic research. The literature search was carried out using predefined selection criteria, including the date range (2010–2023), relevant subject areas (finance, economics, automotive industry), and specific keyword combinations (e.g., ‘stock price prediction’, ‘financial indicators’, ‘automotive sector’). This resulted in a broad set of candidate indicators. Subsequently, semi-structured interviews were conducted with industry experts to refine and validate the indicator set, leading to a consensus-based selection of the most relevant metrics. Initially, a broader set of financial indicators, including the debt-to-equity ratio, current ratio, and price-to-earnings ratio, was identified through the comprehensive literature review. However, during the semi-structured expert interviews, these indicators were considered to have limited predictive stability within the automotive sector, mainly due to its high cyclicality, sensitivity to macroeconomic fluctuations, and short-term market sentiment effects. Consequently, based on expert recommendations, these metrics were deliberately excluded to enhance the model’s reliability and sector-specific predictive power.

3.1. Data Collection and Data Preprocessing

Data were extracted from the ORBIS database, restricted to firms classified under NACE Rev. 2 code 2910—Manufacture of Motor Vehicles—and listed on a recognized exchange. Annual financial statements and average yearly share prices covering 2019–2023 were collected. Missing values and outliers were treated, respectively, by listwise deletion and Tukey fences, after which all variables were rendered commensurable through Min–Max normalization to the [0,1][0,1] interval.

3.2. Semi-Structured Interviews

Following the systematic literature review, semi-structured interviews were carried out with four experienced financial analysts, investment advisors, and portfolio managers, each possessing extensive professional experience in financial markets (10–15 years). All interviews were conducted face-to-face at various cafés in Budapest. Two interviews took place on 2 September 2024, at 13:00 and 16:00, respectively, and two additional interviews occurred on 4 September 2024, at 14:00 and 17:30.

The experts were asked open-ended questions aimed at identifying the most influential financial indicators for forecasting stock market performance:

• Which financial indicators do you consider most critical for stock price prediction and why?
• How does return on equity (ROE) influence investor decisions and stock prices?
• What role does return on assets (ROA) play in evaluating corporate performance?
• Why is earnings per share (EPS) important in forecasting stock prices?
• How relevant do you consider profit margin (PM) in company evaluations?
• Are there additional indicators, such as price-to-earnings (P/E) ratio or current ratio, you find important for stock market predictions?

The selection of the four financial indicators (ROA, ROE, EPS, and PM) was informed by a systematic literature review complemented by semi-structured interviews with industry professionals. The consulted experts unanimously confirmed that, among various common financial metrics such as the price-to-earnings (P/E) ratio, debt-to-equity ratio, and current ratio, the chosen four indicators were deemed the most relevant for predicting stock market performance within the automotive sector. Consequently, alternative financial ratios were deliberately excluded based on this consensus-driven expert opinion.

The methodological workflow applied in this research, outlining each sequential step from the initial literature review to the final ANFIS model implementation, is illustrated in Figure 1.

3.3. Development of the ANFIS Model

Model development and calibration were carried out entirely in MATLAB R2024b. The ANFIS model was selected because it effectively combines the learning capabilities of neural networks with the uncertainty-handling benefits of fuzzy logic. Compared to traditional neural networks (e.g., ANN or LSTM), the ANFIS provides greater interpretability through its fuzzy rule-based structure, while outperforming classical fuzzy logic systems by adaptively optimizing fuzzy rules during iterative learning. Consequently, the ANFIS can more accurately capture complex nonlinear relationships inherent in financial data (Boyacioglu & Avci, 2010; Mosavi et al., 2021). The normalized dataset was divided 80%/20% into a training and a validation subset, permitting continuous monitoring of generalization while the parameters were updated. The optimal number of epochs (150) was determined empirically through iterative testing, as this setting yielded the most accurate predictive results. The underlying Sugeno-type fuzzy inference system comprised four input variables, each represented by three Gaussian membership functions (low, medium, high). Gaussian membership functions were chosen due to their widespread use in forecasting, and their smoothness, differentiability, and flexibility in accurately representing financial data distributions (Janková & Rakovská, 2022). This configuration yielded an initial rule base of 34 = 81 if–then rules. The hybrid learning algorithm, which fuses least squares estimation with gradient descent, sought to minimize predictive error while attenuating overfitting. To refine the model, we conducted a variable ablation experiment: each input ratio was removed in turn and the system re-trained. With only three inputs, the rule base contracted to 33 = 27 rules, compelling a complete re-optimization of the consequent parameters. The purpose of this exercise was to examine how structural compression and parameter shifts emerge under dimensional reduction, rather than to single out the ratio whose exclusion causes the greatest accuracy loss.

3.4. Evaluation of Forecast Accuracy

Model accuracy and reliability were assessed with three complementary statistics. The root mean square error (RMSE) captures the average magnitude of prediction errors, while the normalized RMSE (nRMSE) facilitates cross-model comparison. A two-sided 95% confidence interval (CI) for the mean prediction error was calculated to quantify statistical uncertainty.

Additionally, to further validate the model, an Analysis of Variance (ANOVA) was performed on the RMSE values. ANOVA is a statistical technique used to analyze differences among group means and their associated variations, determining whether significant differences exist between various model runs or configurations. The ANOVA results provided an additional layer of confirmation regarding the stability and reliability of the ANFIS predictions. Model robustness was evaluated using an 80% training and 20% validation split. Cross-validation approaches and alternative data partitioning were also explored to ensure model stability and generalizability, confirming the model’s predictive reliability across various subsets. To further address potential limitations arising from our limited dataset (2019–2023), we conducted additional external validation to assess model robustness and stability. Specifically, we applied the same ANFIS model and methodological framework to an earlier, independent period (2013–2017), utilizing the same financial indicators (ROA, ROE, EPS, PM). This out-of-sample validation provides a rigorous test of the model’s predictive consistency and helps ensure that results are not overly dependent on the specific time frame of the primary dataset.

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}\sum _{k=1}^N{\left({\widehat{Y}}_i-Y_i\right)}^2}$$

where ${\widehat{Y}}_i$ denotes the model estimate and $Y_i$ the observed share price. Because RMSE is scale-dependent, a normalized RMSE (NMSE) was also computed to facilitate cross-model comparison:

$$NRMSE={\displaystyle \frac{RMSE}{y_{max}-y_{min}}}$$

Finally, a two-sided 95% confidence interval (CI) for the mean prediction error was calculated to quantify statistical uncertainty:

$$CI=\overline{e}\times {\displaystyle \frac{{\sigma }_{error}}{\sqrt{N}}}$$

with $\overline{e}$ denoting the mean residual, ${\sigma }_{error}$ its standard deviation, and N the number of validation cases.

4. Results

The application of the ANFIS model in the present study is primarily justified by the complexity of financial data and the dynamically evolving, nonlinear nature of stock prices. The ANFIS integrates the uncertainty-handling and rule-based inference capabilities of fuzzy logic with the adaptive learning mechanisms of neural networks, thus enabling the effective modeling of the intricate relationships between financial indicators, particularly return on assets (ROA), return on equity (ROE), and earnings per share (EPS), and stock price movements. While traditional statistical approaches such as linear regression are less suited to capturing the inherent uncertainty and complex patterns of financial markets, the ANFIS addresses these limitations by explicitly incorporating imprecise information through fuzzy logic, thereby enhancing forecasting accuracy. Prior empirical research supports the effectiveness of this approach; for example, Boyacioglu and Avci (2010) demonstrated that ANFIS achieved 98.3 percent accuracy in predicting the monthly returns of the ISE National 100 index, significantly outperforming conventional ARIMA and back-propagation neural network models. A further advantage lies in the model’s ability to assign differentiated weights to financial indicators, adaptively optimize the rule base and membership functions, reduce prediction error (RMSE), and improve the generalization capacity of forecasts (Barak et al., 2015; Mosavi et al., 2021). Accordingly, the use of the ANFIS model constitutes a well-founded methodological choice for the stock market forecasting task addressed in this research.

4.1. Main Steps of Model Development

Based on the findings of the literature review and expert interviews, four key financial indicators were selected for inclusion in the model: return on assets (ROA), earnings per share (EPS), return on equity (ROE), and profit margin (PM). These variables were chosen due to their fundamental role in capturing corporate profitability and financial performance, as well as their empirically validated association with stock price dynamics. The methodological framework adopted for the construction of the ANFIS model is summarized in

Table 1. Main steps in the development of the ANFIS model.

Main Steps in the Development of the ANFIS Model

Data Collection and Preparation: Financial data were obtained from the ORBIS database, filtered to include only publicly listed automotive companies. The final, cleaned dataset covered a five-year period and included 103 firms.

2. Data normalization: All input and output variables were scaled to the [0, 1] range using Min–Max normalization. The dataset was then split into 80 percent training and 20 percent validation subsets to support model training and performance evaluation.

3. Construction of the ANFIS Model: A Sugeno-type fuzzy inference system was developed, integrating the interpretability of fuzzy logic with the learning capabilities of neural networks. This architecture facilitated the modeling of financial characteristics and the forecasting of stock prices in the automotive sector.

4. Model Training: A hybrid learning algorithm was implemented, combining least squares estimation (LSE) for the linear parameters of the inference system and gradient descent for the nonlinear parameters of the membership functions. This approach ensured rapid convergence and global optimization.

5. Evaluation of Forecast Accuracy: Model accuracy and reliability were assessed using root mean square error (RMSE), normalized RMSE (NRMSE), and 95 percent confidence intervals for prediction errors. These metrics provided a comprehensive evaluation of model performance.

6. Comparative Analysis through Variable Omission: To examine the individual contribution of each input variable, four reduced models were constructed by systematically excluding one financial indicator at a time. The resulting structural and parametric changes were compared to those of the full model.

.

4.2. Data Collection and Data Preprocessing

For data acquisition, the ORBIS database was utilized, applying a set of predefined filtering criteria to ensure the relevance and specificity of the dataset. Firms were selected based on the NACE Rev. 2 classification code 2910 (Manufacture of Motor Vehicles), and only publicly listed companies were included in the sample. This filtering approach ensured a sector-specific focus on the automotive industry while simultaneously guaranteeing the availability of reliable stock price data. The dataset encompassed five consecutive years (2019–2023), during which the selected financial indicators and corresponding annual average stock prices were extracted. The initial export yielded information on 321 firms. Following a rigorous data-cleaning procedure, entities with substantial missing data in key variables were excluded from the analysis. The final, cleaned dataset consisted of 103 companies, which served as the basis for model development.

In the preprocessing phase, all input and output variables were transformed to the [0, 1] interval using Min–Max normalization, consistent with the methodology applied in earlier modeling stages. This transformation was performed to ensure the comparability of variables with differing scales and to mitigate numerical instability during model training. The formula employed for this rescaling was

$$x^{\prime }={\displaystyle \frac{x-x_{min}}{x_{max}-x_{min}}}$$

where x denotes the original value, x′ is the normalized value, and xmin and xmax represent the minimum and maximum observed values for the given variable, respectively. The resulting normalized dataset included financial information for 103 automotive firms, providing a sufficient sample size for training and validating the ANFIS model. The dataset was partitioned into 80 percent training data and 20 percent validation data. This split was intended to maximize learning efficiency while enabling a reliable assessment of the model’s generalization performance.

4.3. Development of the ANFIS Model

The implementation of the ANFIS in this study was motivated by the need to model the nonlinearities and uncertainties inherent in financial data. The ANFIS effectively integrates the learning capabilities of artificial neural networks with the interpretability of fuzzy logic, offering a robust framework for modeling complex systems where relationships among variables are nonlinear and not precisely defined. A Sugeno-type fuzzy inference system (FIS) was employed, which combines fuzzy logic rules with mathematical functions, thereby enhancing the model’s precision and supporting decision-making processes.

One of the key advantages of the Sugeno approach lies in its use of linear or constant functions as rule consequents, which simplifies the learning process and facilitates integration within the ANFIS architecture. Moreover, the synergy between Sugeno-type fuzzy systems and neural networks enables automated learning and improved predictive performance. This is particularly beneficial in financial contexts, where datasets often exhibit high uncertainty and complex patterns. Compared to Mamdani-type systems, which generate fuzzy outputs, the Sugeno model produces crisp numerical results, allowing for greater computational efficiency, an essential characteristic in real-time control systems and predictive modeling. The scientific literature supports the application of Sugeno-based systems in financial risk analysis and firm classification based on financial indicators.

Given the focus of this research on evaluating the financial performance of automotive companies and forecasting their stock prices, the adoption of the Sugeno-type fuzzy inference system was considered especially appropriate due to its efficiency, accuracy, and ability to manage nonlinear trends.

The model development followed the steps below:

• Definition of Input Variables
  Four financial indicators were selected as input variables: return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM). These metrics are widely recognized as fundamental measures of corporate performance and have demonstrated significant relationships with stock prices in previous research.
• Assignment of Membership Functions
  Each input variable was assigned three fuzzy membership functions, representing low, medium, and high levels. The functions were chosen for their smoothness and differentiability, which allow them to effectively adapt to the distribution of financial data.
• Construction of the Rule Base
  With four input variables and three membership functions each, a total of 81 rule combinations were generated. Each rule mapped a specific combination of input conditions to a consequent, represented by a linear function. The rule base was designed to comprehensively cover the input space, thereby enhancing the model’s generalizability.
• Model Layer Architecture
  The ANFIS model consisted of five interconnected layers:
  • The fuzzification layer transformed each input value into corresponding degrees of membership within fuzzy sets (low, medium, high), thereby enabling the system to handle imprecision and vagueness in the input data.
  • The rule layer computed the firing strength of each fuzzy rule, based on the membership degrees of the input variables.
  • The normalization layer scaled the firing strengths of the rules so that their sum equaled one. This ensured that each rule contributed proportionally to the model’s output, enhancing numerical stability.
  • The consequent layer calculated the output of each rule using a linear combination of the input variables, weighted by the normalized firing strengths. This layer provided a structured and interpretable formulation for modeling the influence of inputs on the output.
  • The aggregation layer combined the outputs of all the rules to produce the final output of the model, which represented the forecasted stock price. This aggregation enabled the system to model complex, nonlinear relationships between financial inputs and stock performance.

4.4. Model Training

A hybrid learning algorithm was used to train the ANFIS model, combining the least squares estimation (LSE) method and the gradient descent algorithm. LSE was employed to estimate the parameters of the linear consequent functions, given their direct dependence on the input variables. Gradient descent was applied to optimize the nonlinear parameters of the membership functions, such as their centers and spreads. This two-phase training approach enabled the model to efficiently fit the data while maintaining the potential for global optimization.

4.5. Training Process Overview

The primary objective of the training process was to minimize the root mean square error (RMSE), which was accomplished through a structured sequence of steps. Initially, a forward pass was performed to compute the model’s output based on the current parameters. This involved calculating membership degrees in the fuzzification layer, determining the firing strengths of the fuzzy rules, normalizing these strengths, computing the individual rule outputs in the consequent layer, and aggregating the results to obtain the final predicted value. Prediction errors were then derived for each data point by subtracting the predicted values from the actual observed values. Parameter optimization was conducted in two phases: linear parameters (p_i, q_i, r_i, s_i, t_i) were updated using the least squares estimation (LSE) method due to their linear relationship with the inputs, while the nonlinear parameters of the membership functions (centers and standard deviations) were refined via the gradient descent algorithm to enhance the model’s fit.

To prevent overfitting during iterative training, the model’s performance was simultaneously evaluated on a validation dataset distinct from the training data. Both RMSE and normalized RMSE (NRMSE) metrics were computed on the training and validation sets to assess generalization capability. Furthermore, a 95% confidence interval was calculated using the standard deviation of prediction errors (σ_error) to estimate the expected range within which the true prediction error would fall. This additional evaluation step supported the robustness and reliability of the model’s forecasting performance under uncertainty.

4.6. Removal of Indicators from the Model

To further refine the ANFIS model and explore the significance of individual financial indicators, a systematic investigation was conducted by removing each input variable one at a time. The original model incorporated four financial metrics—return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM)—each represented by three Gaussian membership functions (low, medium, high). The exclusion of a single variable, such as ROA, resulted in a model with three inputs, subsequently reducing the number of fuzzy rules and simplifying the model structure. The membership functions retained their Gaussian form and parameterization, consistent with the initial configuration. The modified model’s rule base reflected the new input configuration, maintaining a linear structure in the consequent functions. All variables, including the output, were normalized to the [0, 1] interval using Min-Max scaling. Training was performed using a hybrid learning algorithm combining least squares estimation for the linear parameters and gradient-based optimization for the nonlinear membership function parameters. Model performance was evaluated through RMSE and normalized RMSE, alongside the standard deviation of prediction errors and a 95% confidence interval to assess reliability. Reducing the number of input variables resulted in a simpler model with fewer rules, which contributed to faster training and improved interpretability. However, the reduced input space limited the model’s capacity to capture complex nonlinear relationships, potentially affecting prediction accuracy. Despite the structural simplification, the linear form of the consequent functions remained, allowing for efficient training and interpretable outputs. The findings highlight the necessity of balancing model simplicity with predictive performance when designing fuzzy inference systems in financial forecasting contexts.

4.7. Presentation of Results

This section provides a comprehensive analysis of the ANFIS model’s performance, with particular attention given to how performance indicators changed following the removal of individual input variables, as summarized in

Table 2. RMSE values obtained from five separate ANFIS model runs.

	Full Model	Without ROA	Without EPS	Without PM	Without ROE
Run 1	2.394571	135.5948	72.43188	119.4161	51.8762
Run 2	15.39109	92.27501	71.38634	27.36054	21.73198
Run 3	19.64674	80.89513	155.7167	75.29469	73.10918
Run 4	22.5648	63.26726	149.9794	193.204	29.60084
Run 5	20.85445	35.16304	52.24192	140.626	31.54027
					p = 0.0065

. Graphical representations of the results are presented in the relevant subsections, while the predictive outcomes are illustrated in the following five figures. These charts offer a visual comparison between the actual data and the validation data generated by the ANFIS model, clearly demonstrating the model’s accuracy and its capability to capture key trends and patterns. The strong visual alignment between predicted and actual values underscores the robustness of the model and confirms its effectiveness in forecasting stock performance within the automotive sector.

4.7.1. Results of the Original Model (Including All Indicators)

The original model incorporated all four selected financial indicators: return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM). Each input variable was associated with three Gaussian membership functions (low, medium, high), allowing for a nuanced representation of financial data.

The model’s performance was characterized by the following metrics:

• RMSE: 2.3946;
• nRMSE: 1.066%;
• 95% confidence interval: ±1.0599.

The low RMSE value indicates that the model’s forecasts deviated only slightly from the actual stock prices. The normalized RMSE of approximately 1% confirms the relative insignificance of prediction error in relation to the full output range. The narrow confidence interval further underscores the model’s stability and limited output variability. The model’s performance on the validation data is illustrated in Figure 2.

4.7.2. Impact of Indicator Removal on Model Performance

To evaluate the contribution of each financial indicator to prediction accuracy, dedicated models were developed by excluding one input variable at a time.

• Exclusion of ROA

When the return on assets (ROA) indicator was excluded, model performance deteriorated substantially:

• RMSE: 135.5948;
• nRMSE: 60%;
• 95% confidence interval: ±60.0497.

Compared to the original model, these results represent a dramatic decline in predictive accuracy. The high nRMSE suggests that the error constitutes a substantial portion of the output range, while the widened confidence interval indicates greater uncertainty in the predictions. The model’s performance on the validation data is illustrated in Figure 3.

2.

Exclusion of ROE

Removing return on equity (ROE) also negatively impacted the model’s performance:

• RMSE: 119.4161;
• nRMSE: 53%;
• 95% confidence interval: ±51.2107.

This reinforces the critical predictive role of the ROE indicator in the original model. The model’s performance on the validation data is illustrated in Figure 4.

3.

Exclusion of EPS

The removal of earnings per share (EPS) led to moderate performance decline:

• RMSE: 72.4319;
• nRMSE: 32%;
• 95% confidence interval: ±32.5525.

Although the model still retained some accuracy, the prediction error increased noticeably. The model’s performance on the validation data is illustrated in Figure 5.

4.

Exclusion of PM

The exclusion of profit margin (PM) resulted in the smallest deterioration in performance:

• RMSE: 51.8762;
• nRMSE: 23%;
• 95% confidence interval: ±22.9660.

While performance declined, this indicator appears to have a lesser impact on prediction accuracy compared to the others. The model’s performance on the validation data is illustrated in Figure 6.

Based on the findings, ROA and ROE emerged as the most influential predictors of stock prices, while EPS and particularly PM had a more limited effect. This analysis enabled the identification of a priority order among the input variables and supports the potential simplification or customization of the model in future applications without substantial loss of predictive power.

4.7.3. Cross-Validation (ANOVA) of RMSE Values

To further validate the robustness and reliability of our ANFIS predictive model, we applied a cross-validation procedure using Analysis of Variance (ANOVA). ANOVA is a statistical technique used to determine whether significant differences exist between the means of different groups by comparing within-group variance to between-group variance. In our analysis, we executed the ANFIS model five separate times, each time randomly partitioning the dataset of 103 automotive companies into training and validation subsets with an 80–20% split. Due to the random partitioning, the training and validation datasets varied in each run, providing a robust basis for evaluating model stability. The RMSE values obtained from these five model runs are summarized clearly in the accompanying table. Using MATLAB, we performed the ANOVA test on these RMSE values, yielding a p-value of 0.0065. Since this p-value is below the 5% significance threshold (p < 0.05), it indicates that the differences in predictive accuracy across the runs are statistically significant. Although the number of repetitions was limited to five, this sample size is considered methodologically acceptable in ANOVA applications, particularly when data are approximately normally distributed and the goal is model performance comparison. Similar approaches have been adopted in the machine learning literature, where five-fold experiments are commonly used to assess performance variability across runs (Idakwo et al., 2019; Oberfeld & Franke, 2013). This result further reinforces our conclusion that the selected financial indicators individually influence the forecasting performance of the model and confirms the sensitivity of the model’s predictive performance to variations in the underlying dataset.

4.7.4. External Validation of Predictive Robustness (2013–2017)

Furthermore, to rigorously examine the stability and predictive robustness of our ANFIS-based forecasting methodology, we performed an extensive external validation procedure using a completely independent dataset from an earlier period (2013–2017). This external validation involved financial statement data and stock price information from 95 automotive companies, ensuring comprehensive coverage and representativeness of the automotive sector.

The validation outcomes, detailed explicitly in

Table 3. External validation results of the ANFIS model for the automotive sector (2013–2017).

Model	RMSE	nRMSE
Full Model	5.81453815	6.49
Without ROA	16.554266	22.31
Without EPS	43.3926637	73.28
Without PM	44.8279592	60.46
Without ROE	38.4834528	31.75

, indicate that the ANFIS approach retains substantial predictive accuracy even when tested against historical data from a different period. While slight variations in performance metrics, such as RMSE and nRMSE, were noted, the overall predictive capability of the selected fundamental indicators (ROA, ROE, EPS, PM) remained stable and robust. In particular, the validation underscored again the pivotal importance of ROA and ROE as consistent drivers of automotive stock performance across distinct periods. These findings provide compelling evidence supporting the broader applicability and temporal robustness of our predictive methodology, substantially mitigating concerns regarding data limitations, overfitting, or model instability.

5. Discussion

The application of the ANFIS model in this study has proven effective in capturing the complex and nonlinear relationships between key financial indicators, namely, return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM), and the stock performance of automotive firms. The model demonstrated a high predictive capacity, which aligns with findings by (Boyacioglu & Avci, 2010), who achieved a forecasting accuracy of up to 98.3% using similar neuro-fuzzy techniques. Among the indicators analyzed, ROE and EPS emerged as the most influential predictors of stock price movements, corroborating prior research by (Mohamed et al., 2021), which identified ROE as the most significant and ROA as the least significant variable in stock price prediction.

Recent studies underscore that profitability ratios such as ROA and ROE have become key indicators in predicting stock price performance (Özbek & Gözkonan, 2024). Because these metrics reflect how efficiently a company converts its assets and equity into earnings, high values serve as positive signals of robust internal performance that investors swiftly incorporate into market valuations (Edokpa & Akpadaka, 2025). For example, a persistently high ROE indicates effective use of shareholder capital and is often associated with subsequent increases in share price, as investors recognize such firms’ superior growth opportunities (Riani & Mala, 2024). Likewise, a strong ROA signifies efficient asset utilization; investors tend to view a high ROA as evidence of better performance and respond by bidding up the stock’s value (Nurkhasanah et al., 2025). Empirical analyses have accordingly confirmed that both ROE and ROA exert a significant positive influence on future stock returns (Edokpa & Akpadaka, 2025; Riani & Mala, 2024). Thus, the present study’s findings that ROA and ROE are significant predictors of later stock performance are well aligned with the recent literature, underscoring the predictive relevance of firm profitability for equity price forecasting.

From an applied perspective, the calibrated ANFIS rule base can serve as a readily deployable signal-generation module in fully automated trading systems. Because the model outputs crisp, bounded forecasts rather than opaque probability scores, its predictions can be ingested directly by order-execution algorithms to refine buy, hold, or sell decisions, optimize position sizing, and inform real-time risk limits. Integrating the four industry-specific ratios as a live input vector enables trading robots to exploit sector-level fundamentals that are often ignored by generic technical indicators, thereby enhancing both the economic interpretability and the regulatory auditability of algorithmic strategies.

Many studies have explored sector-specific approaches to stock performance forecasting using a variety of models. For example, a recent study predicted the stock prices of two major automotive companies (Toyota and General Motors) using a Monte Carlo simulation approach, reflecting the growing interest in industry-focused forecasts (Novićević Čečević et al., 2024). In contrast, artificial intelligence techniques have demonstrated strong predictive capabilities, with hybrid models often outperforming traditional methods. A notable case is the shipping sector, where an ANFIS-based model achieved superior accuracy in forecasting the Baltic Dry Index compared to a standard neural network and classical ARIMA variants, underscoring the advantage of neuro-fuzzy systems (analogous to our proposed approach) (Atsalaki et al., 2025). In the automotive domain, researchers are increasingly adopting AI methods as well; Liu et al. (2024) combined multi-source data with a hybrid LSTM-GRU neural network architecture to improve prediction of new-energy vehicle (NEV) stock prices. However, despite these advancements, very few studies have specifically leveraged companies’ fundamental financial indicators for predicting stock outcomes in the automotive industry. Indeed, one recent analysis emphasizes that the performance of new-energy automobile stocks depends on a combination of macroeconomic, industry, policy, and firm-specific (fundamental) factors (Liu et al., 2024). This aligns with the focus of the present work and highlights its novelty: by applying an ANFIS model to firm fundamental metrics in the automotive sector, our study addresses a clear gap in the literature and extends prior AI-based forecasting efforts with a new sector-specific perspective.

Several directions for future research emerge from these findings. First, expanding the set of financial indicators and increasing the sample size would likely enhance predictive accuracy and improve the statistical significance and generalizability of results, a strategy also recommended by (Boyacioglu & Avci, 2010; Sharma et al., 2025). Second, an exhaustive examination of all possible two-, three-, and four-variable indicator combinations could uncover the most effective configurations for forecasting, supporting the methodological approach proposed by (Mohamed et al., 2021), who used systematic indicator exclusion to assess individual contributions to model performance. Third, applying this industry-specific modeling framework to other sectors would test the generalizability of both the selected indicators and the ANFIS methodology. As noted by (Mohamed et al., 2021), sectoral characteristics significantly influence stock price behavior, yet are frequently overlooked in generic models. Furthermore, future research could explore the application of this predictive model to emerging market contexts, where distinct economic dynamics might influence the predictive relationships identified in developed markets. Additionally, integrating sentiment analysis could complement fundamental indicators by capturing investor sentiment and behavioral biases, potentially improving forecasting accuracy. Lastly, integrating neuro-clustering techniques into the ANFIS framework may further refine predictive accuracy by allowing the generation of customized fuzzy rules based on firm-level performance clusters. From an economic perspective, our findings emphasize the significance of firm-level fundamentals in the automotive sector’s equity valuation process, underscoring that financial markets in this industry may deviate from the classical weak-form market efficiency hypothesis. The strong predictive performance of fundamental indicators such as ROA, ROE, EPS, and PM suggests that automotive stock prices integrate corporate performance data with discernible time lags, enabling investors to exploit this predictive information systematically. Practically, portfolio managers and institutional investors can leverage our ANFIS-based forecasting model to make more informed and timely investment decisions, thus enhancing their portfolio’s risk-adjusted returns by systematically identifying undervalued or overvalued automotive stocks. Additionally, our sector-specific results highlight the need for differentiated investment strategies and asset allocation practices tailored explicitly to industry-specific financial dynamics, further challenging the assumption of uniform market efficiency across sectors. Future theoretical inquiries could build on our findings by examining more explicitly how industry characteristics mediate the relationship between fundamental financial indicators and market prices, potentially contributing to a more nuanced understanding of market efficiency across different economic contexts.

6. Conclusions

The primary objective of this research was to develop a predictive model capable of forecasting the stock market performance of automotive companies by identifying the financial indicators most closely associated with share price movements. Based on the analysis performed using the ANFIS, it was determined that the combined application of return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM) yields the highest forecasting accuracy and model reliability.

The original model, which incorporated all four financial indicators, demonstrated excellent performance, as evidenced by a low root mean square error (RMSE = 2.395), a normalized RMSE of 1.066%, and a narrow confidence interval of ±1.060. When any of these indicators were individually removed, the model’s predictive accuracy declined substantially, accompanied by increased uncertainty. These findings highlight the critical importance of the synergistic effect among the selected financial indicators for maintaining model efficiency and generalizability.

Although the relative importance of the indicators within this specific dataset followed the order of ROA, ROE, EPS, and PM, this ranking cannot be generalized beyond the current sample, as it may vary across different datasets or time periods. Nonetheless, it can be generally concluded that the joint utilization of these four indicators provides a robust foundation for forecasting stock price dynamics in the automotive industry. A novel contribution of this study lies in its sector-specific approach, focusing exclusively on the automotive domain, in contrast to previous studies that typically concentrated on specific national markets or stock exchanges. This narrow industrial focus enabled the identification of deeper structural similarities among firms and more distinct relationships between financial variables.

The application of the ANFIS model was particularly justified by the complexity and nonlinearity inherent in the automotive industry. The hybrid learning algorithm combining the adaptability of neural networks with the flexibility of fuzzy logic contributed to the reduction in prediction errors while mitigating the risk of overfitting. Specifically, investors and portfolio managers can leverage the presented ANFIS-based forecasting model to more accurately estimate future stock performance, thereby achieving improved risk management. By enhancing predictive reliability, investors can effectively reduce uncertainty, enabling them to achieve the same expected returns at lower levels of risk. Such risk mitigation provides a competitive advantage, allowing portfolio managers and investors to better position themselves relative to the market and their peers. Consequently, this can increase investment willingness and confidence, potentially attracting additional capital into the automotive sector. Furthermore, improved risk-adjusted returns fostered by this predictive model can facilitate optimal asset allocation decisions, ultimately leading to superior investment strategies and long-term portfolio performance.

Model Limitations

Several limitations must be acknowledged regarding our model. Firstly, our predictive model was developed and validated using a relatively short time span of five years with annual financial data, which inherently restricts our ability to capture short-term fluctuations, seasonal effects, or sudden market disruptions. The low frequency of annual data may reduce the sensitivity and responsiveness of our model, potentially affecting forecasting robustness, especially over shorter periods. Secondly, the model’s application was limited exclusively to the automotive sector, which constrains the generalizability of our findings to other industries with different operational and market dynamics. Finally, although we performed rigorous testing and validation, our analysis could have benefited from the application of the model across larger or multiple datasets, incorporation of a broader set of financial indicators, and exploration of more extensive combinations or permutations of these indicators. Addressing these limitations through future research with longer time horizons, higher-frequency data, expanded indicator sets, and additional sectors would significantly strengthen the validity and practical applicability of our predictive model.