Stock Prediction with a Neuro-Fuzzy Model Using Financial and Accounting Indicators Thorough Data from Budapest Stock Exchange

Abstract

The large-scale economic growth experienced in Hungary and Central-Eastern Europe over the past 8 years has made this region attractive to many investors. However, predicting stock price developments is a challenge for investors. The tools and methods that can provide accurate information about the stock prices of these countries are crucial during the prediction. Many different factors can affect stock price forecasting, such as company fundamentals and internal (earnings per share (EPS), dividends per share and book value) and external factors (government rules and regulations, inflation and other macroeconomic conditions such as .gross domestic product (GDP), money supply, oil price fluctuations and environmental conditions). Many researches have already focused on the issues of stock price forecasting, from the traditional approach to the latest data mining applications. However, these studies cannot be standardized because there is no accurate and perfect model that predicts the exact movement of stock prices. While previous studies have considered both internal and external factors that affect stock price forecasting, this research considers the impact of company performance variables and applies a neuro-fuzzy model to predictive stock price estimation. Furthermore, previous studies focused on the internal and external determinants of stock prices and examined the relationship between different variables and stock prices. In contrast, this study takes into account the advantages of previous methods and models and tries to synergize their advantages while minimizing their disadvantages. The study contributes to the financial literature of the financial markets of Central and Eastern European countries, especially Hungary, as it focuses on performance indicators and ranks their predictability.

Intorduction

The unique contribution of neurofuzzy systems to the forecasting of financial markets results from the combination of neural networks and fuzzy logic. Neural networks are models that mimic the operation of the human brain, capable of „learning” and „understanding” complex patterns and relationships in data. Like the brain, neural networks have „neurons” that connect and interact with each other, enabling the discovery of complex patterns. The adaptive capability of neural networks, i.e., their ability to learn and adapt, is particularly valuable in forecasting financial markets, where trends and relationships often change. Fuzzy logic, on the other hand, unlike classical (or „sharp”) logic, can handle uncertainty and fuzzy, ambiguous information. The basis of fuzzy logic is the concept of „fuzzy sets”, in which elements belong to the set to a certain extent, with a value between 0 and 1, not only unambiguously (yes/no). This allows for modeling uncertainties and ambiguous information frequently occurring in the real world.

This combination of two techniques – neural networks and fuzzy logic – forms neurofuzzy systems. These systems can „learn” similarly to neural networks, while they can handle uncertainty and ambiguous information with the help of fuzzy logic. This combination is especially advantageous in forecasting financial markets, where patterns are often complex and changing, and where uncertainty and ambiguous information often occur. Therefore, neurofuzzy systems can model the complex, non-linear relationships of financial markets and provide better predictions.

Fundamental analysis involves examining the basic economic and financial indicators of companies to determine the company’s real, „fundamental” value. Neurofuzzy models enable the integration of many aspects of fundamental analysis and the use of this complex information in price forecasts. Identifying the financial and accounting indicators that can best predict future price movements is critical for neurofuzzy models. These indicators typically include company profitability, debt/EBITDA ratio, indicators of financial stability, and others. Neurofuzzy models can use these indicators to „learn” about the behavior of companies and markets and to „understand” the complex relationships between the indicators and prices. This capability of neurofuzzy models is made possible by the so-called „adaptive ability”. This means that the models can modify the weights and rules based on which the indicators are used in price forecasts, based on experience. For example, if a particular indicator (e.g., debt/EBITDA ratio) has better predicted price movement in the past, the model can increase the weight of this indicator in future forecasts.

This adaptive capability is particularly important in financial markets, where trends and relationships often change. Neurofuzzy models are capable of „learning” about these changes and continuously updating their models to improve forecast accuracy. This allows the models to respond to market changes and new information and improve the accuracy of forecasts over time. Our research focuses on examining the efficiency of neurofuzzy methods on the Budapest Stock Exchange.
Our aim is to discover which financial and accounting indicators can be most effectively used to maximize the accuracy of the neurofuzzy method when predicting stock prices. The research focuses on fundamental indicators such as companies’ profitability, debt/EBITDA ratios, indicators of financial stability, and similar data. We predictively analyze these data using neurofuzzy models that can recognize and utilize patterns hidden in complex non-linear relationships. Our aim is to further develop knowledge about these models, particularly in terms of the key factors influencing model accuracy. The significance of our research stems from several reasons. First, by making financial market predictions more accurate, we can increase market efficiency and investor confidence. Second, accurate forecasts can improve policymakers’ ability to maintain economic stability and manage various financial risks. Third, the research can contribute to the development of artificial intelligence and machine learning applications in financial forecasting. In addition, another important aspect of our research is to compare the results of the Budapest Stock Exchange with the results of other international stock exchanges. Such comparisons can help reveal differences between markets and those specific financial and accounting indicators that have varying impacts on the accuracy of price forecasts in different markets. The results of the research may therefore be useful not only for the Budapest Stock Exchange but also for other international stock exchanges.

Literature review

The stock market is a complex system where individuals either generate profits or incur losses (Aparna Nayak, M. M. Manohara Pai, Radhika M. Pai, 2016). In recent years, with the rapid advancement of the economy and the drastic popularity of stock market trading, an increasing number of people have begun investing in the stock market. This is mainly because transactions involving billions of dollars worth of assets take place daily on the stock market (Seyed Taghi Akhavan Niaki, Saeid Hoseinzade, 2013).
Forecasting in the stock market is hence of paramount importance and a significant area of research in the financial domain since investing in the stock market carries a higher degree of risk (Gourav Kumar, Sanjeev Jain, and Uday Pratap Singh, 2021). Accurate prediction of stock price changes can mitigate the investment risk of stock investors and efficiently enhance the return on investment (Wenjie Lu, Jiazheng Li, Jingyang Wang, and Lele Qin, 2020). The creation and evaluation of stock market forecasts are essential for investors and financial professionals. Forecasts should assist investors in better understanding market trends and anticipated market changes, thus enabling them to effectively manage their portfolios and improve the investment returns they achieve. Predicting the value of stock groups has always been appealing and challenging for shareholders due to its inherent dynamics, nonlinearity, and complex nature (M. Nabipour, P. Nayyeri, H. Jabani, A. Mosavi, E. Salwana, and Shahab S., 2020) (Gourav Kumar, Sanjeev Jain, and Uday Pratap Singh, 2021).
Stock market forecasting is an attempt to predict the potential direction of stock movement. This provides investors with the opportunity to try to speculate about expected price movements and decide on their investments accordingly. Numerous factors contribute to stock price fluctuation, including macroeconomic factors, market expectations, and trust in corporate governance and operations. The advancement of technology allows the public to access larger amounts of information in a timely manner. This implies that stock analysis is becoming increasingly challenging as a significant amount of data needs to be processed in a relatively short period (Dev Shah, Haruna Isah, Farhana Zulkernine, 2019).
There are two main approaches to the analysis of financial markets: technical and fundamental analysis.
Fundamental analysis primarily relies on three fundamental aspects.
– macroeconomic analysis such as Gross Domestic Product (GDP) and Consumer Price Index (CPI), which assess the impact of the macroeconomic environment on a company’s future profits,
– industry analysis, which estimates a company’s value based on industry status and prospects.
– corporate analysis, which evaluates a company’s current operations and financial condition to assess its intrinsic value. (Dev Shah, Haruna Isah, Farhana Zulkernine 2019)
Technical analysis takes into account sentiment, cash flow, raw data, trends, quantity, and cycle. (Dev Shah, Haruna Isah, Farhana Zulkernine 2019) Forecasting stock values has always been a challenging task due to its long-term unpredictability. The Efficient Market Hypothesis holds that it is impossible to predict stock values, and that stock movements are random. However, the latest technical analyses show that most stock values are reflected in previous records; therefore, movement trends are crucial for effective forecasting. (M. Nabipour, P. Nayyeri, H. Jabani, A. Mosavi, E. Salwana, and Shahab S. 2020) Accurate forecasting of stock market returns is a major challenge due to the volatile and nonlinear nature of financial equity markets. With the introduction of artificial intelligence and increased computational capabilities, programmed forecasting methods have proved more effective in predicting stock prices. (Mehar Vijh, Deeksha Chandola, Vinay Anand Tikkiwal, Arun Kumar 2020) Based on the studies examined, artificial intelligence may be suitable for stock market forecasting. Artificial Intelligence (AI) is a computer system that aids in the resolution of tasks that could be solved with human intelligence. Its goal is to solve problems that would be difficult or impossible for a human to solve. (Ahmad, Kharil, Shujaat, Mansoor, and Irfan 2021) (McCarty, Minsky, Rochester, Shannon 1953) The main areas of AI include natural language processing, vision and scene recognition, intelligent computer-assisted instruction, and neural informatics. (Avneet Pannu 2015) This system is a dynamically developing technology that impacts multiple areas of life. Various techniques, such as neural networks, are used in AI. (Avneet Pannu 2015)
Neural Networks are a mathematical structure represented by a computer model based on brain functions. The neural elements have an input value, which is evaluated by the agent based on computations and provide an output value, which is responsible for decision-making. (Ghosh-Dastidar and Adeli 2009) Neuro-Fuzzy is a system based on neural networks and fuzzy logic. Neuro-Fuzzy combines the best properties of its two elements to achieve the best system. (Babuška and Verbruggen 2003) Neural networks are capable of solving computational tasks, while the Fuzzy system can handle uncertainties. Neuro-Fuzzy can be used in various areas such as machine learning, forecasting future processes, and developing rule-based systems. (Janková and Dostal 2020) Fuzzy logic, used in Neuro-Fuzzy as well, is a logical system that serves to handle doubtful or uncertain expressions and decisions. Fuzzy systems serve to solve problems occurring in the real world that are difficult or impossible to solve with traditional, binary logic. (Liu and Jeffery 2020)
The aforementioned Neuro-Fuzzy model can be applied to stock market forecasts. (Janková and Dostal 2020) (Mohamed, Ahmed, Mehdi, Hussain 2020) The Neuro-Fuzzy method can combine various data, including past prices, trading factors, and fundamental factors, to give a forecast on short-term trends and thus assist business decision-makers and investors in their decision-making process (Atsalakis and Valavanis 2009) Financial ratios derived from balance sheet and income statement data, such as Return on Equity (ROE), Profit Margin (PM), Earnings Per Share (EPS), and Return on Assets (ROA), could be suitable for stock market forecasting using the Neuro-Fuzzy approach. ROE (Return on Equity), a measure of return on equity, is a pertinent indicator in stock market forecasting. The PM (Profit Margin), the net profit margin as a proportion of revenue, and EPS (Earnings Per Share), the net income per share, are also important indicators for stock market forecasts. However, ROA (Return on Assets), the profitability ratio that indicates the profit per unit of assets, is not a relevant measure for stock market forecasting using the Neuro-Fuzzy method. (Mohamed, Ahmed, Mehdi, Hussain, 2020)
The ANFIS model could be an effective tool for predicting stock indices in Central European countries. Among the Visegrad Group, the Neuro-Fuzzy model proved to be most efficient in predicting the Hungarian BUX index, with a prediction error rate of 0.79%. Based on the analysis, it was concluded that the ANFIS is more teachable and more efficient for forecasting lesser liquid companies (Janková and Dostal, 2020). A combined Neuro-Fuzzy system that integrates decision tree systems can also be used for stock market forecasting. A tree system is a graph where nodes represent decisions or data, and edges represent relationships between the data. The crux of the tree system is the hierarchical decomposition of data by branching them into increasingly finer groups. Combining decision trees with neuro-fuzzy systems provides better results than using the two systems separately. The predictions become more accurate and reliable, as they combine the benefits of both systems. (Nair, Dharini, 2010)

Results

Our research approach appears comprehensive and methodologically sound. We used the MATLAB software to implement the Neuro-Fuzzy model, which allowed us to thoroughly examine the predictive capabilities of input variables within the context of stock price forecasting.
In our model, we effectively employed the subtractive clustering algorithm to initialize membership functions, efficiently segregating the examined data set into pertinent clusters. We applied the ANFIS (Adaptive Neuro Fuzzy Inference System) using Sugeno-reasoning, a widely adopted model in this field. The ANFIS structure comprises five layers beyond the input layers. The hidden layers (1, 2, 3, and 4) represent membership functions and fuzzy rules. The first layer is the fuzzification layer where neurons perform fuzzification. In the Jang (1993) model, the fuzzification neurons utilize the Gaussian activation function (Negnevitsky, 2017). It has been established that the Sugeno neuro-fuzzy algorithm functions optimally with Gaussian-type membership functions (Jain & Martin, 1998). With Gaussian fuzzy sets, the algorithm can exploit all information from the training set, unlike the triangular parts (Jain & Martin, 1998). The second layer is the rule layer where each neuron corresponds to a Sugeno-type fuzzy rule. The third layer is the normalization layer where each neuron accepts data from all neurons of the rule layer and calculates the normalized fire strength of the respective rule. The fourth layer is the defuzzification layer where each neuron connects to its corresponding normalizing neuron and also receives the initial inputs, x and y. The fifth layer consists of a single summarizing neuron that calculates the sum of all defuzzification neuron outputs and generates the aggregated ANFIS output.
We used the Adaptive Network-Based Fuzzy Inference System (ANFIS) parameters to adjust membership functions during the learning process. The ANFIS system allocates a Gaussian membership function to each input variable for each fuzzy cluster. Additionally, it sets a rule for each cluster and assigns a „linear” output membership function to each fuzzy cluster. The MATLAB implementation requires the user to provide the Cluster Influence Range parameter, which varies between 0 and 1. In our research, we applied a Genetic Algorithm (GA) to find this parameter’s optimal value, which minimizes the root mean square error (RMSE). We discovered that the optimal parameter value is 0.08, which is applicable for all input and output membership functions. This is how we established the methodological framework for our research. Our decision to depict the applied neuro-fuzzy method in a general figure (Figure1) is justified due to space constraints and the inability to showcase detailed simulation data and the neural network. Nonetheless, it should still provide a comprehensive understanding of the method employed in our research.
During our research, we utilized 1,160 stock prices to construct, train, and cross-validate our neuro-fuzzy model. Four performance indicators evidently influenced stock price changes over the past five years, as they demonstrated a tight correlation between actual and forecasted stock prices. To measure the accuracy and performance of our predictive models, we employed various statistical techniques. In this study, we used the root mean square error (RMSE) to compare predicted and actual values. To investigate the predictive power of each input variable, we retrained the neuro-fuzzy model by removing only one input variable at a time, then analyzed the generalized RMSE on test data by the model. The larger the increase in RMSE, the more predictive the removed input variable is. The percentage change in RMSE shows the removal of each input variable.
According to our findings, the Return on Assets (ROA) is the least significant factor in predicting stock prices, while the Return on Equity (ROE) is the most crucial predictor, as its removal resulted in a very high change in RMSE (30.4 percent). Both the profit margin (PM) and the Earnings per Share (EPS) play significant, yet equally important roles in predicting stock prices. During this research, we conducted a sensitivity analysis to ascertain the degree to which various input variables influence stock prices. We carried out the sensitivity analysis using the perturbation method (Wang, Jones, & Partridge, 2000). We incremented each input variable in steps of 5%, from 0% to 50%, and calculated the stock price at each step. We computed the changes in stock prices at every step of each input variable.
The analysis showed that all four factors exert a positive, proportional effect on stock prices, with EPS being the most important factor in explaining changes in stock prices compared to the other factors. The following figure (figure 2) illustrates our results.
According to our results, Return on Assets (ROA) is the second most crucial factor, while the Profit Margin (PM) is the least significant. Based on our findings, Earnings per Share (EPS) ranks first in explaining changes in stock prices. This result is understandable given the investors’ perspective, as they focus on the earnings per share. EPS is the best predictor of stock prices, with only a minimal negative change; this seems logical as EPS is a financial indicator that measures the relationship between the net income generated by a company and the number of common shares.
ROA is less important than EPS as investors focus on profitability ratios, not on ROA, which does not directly affect their decisions to sell or buy shares. Our study corroborates the findings of many previous researches such as Zahedi and Rounaghi (2015), Tüfekci (2016), and Dash and Dash (2016), who found that EPS is the most important factor in explaining stock price movements. Our findings are consistent with Umar and Musa (2013),, who also found that stock prices have a significant relationship with both ROE and EPS. Contrarily, our result is completely different from Maryyam (2016), who found that ROA has a significant positive impact on stock returns. The results of our model indicate that the four profitability indicators used in this work significantly contribute to accurate forecasting of stock prices in the United Arab Emirates, as evidenced by the RMSE value of 1.56.

Conclusions

Accurate forecasting of stock prices poses a significant challenge to investors, and numerous tools and models have been developed to support proper investment decisions in stocks. In this study, we investigated the forecasting of stock prices using a NFS (neuro-fuzzy system) and identifying the main factors influencing these using data from the Budapest Stock Exchange. We developed the model with the help of MATLAB’s neuro-fuzzy toolbox, and thanks to the ANFIS (Adaptive Neuro-Fuzzy Inference System) method, we achieved accurate results. We observed a clear correlation between actual and forecasted stock prices.
For the study, we collected and analyzed the data of 15 companies on the Budapest Stock Exchange, with a total of 420 observations over 28 quarters (7 years). We used four performance metrics (ROA, ROE, EPS, and PM) to determine the predictive power of stock prices. Our results showed that ROE was the most significant predictive factor, while ROA had a weaker impact on stock prices. EPS proved to be the most influential profitability indicator on the explanatory side, while PM was the least able to explain fluctuations in stock prices.
Based on these results, it can be concluded that the study has a significant impact on investors, decision-makers, and researchers. It helps researchers in further developing and testing the model in different contexts and supports investors in forecasting stock prices. Despite the fact that the study represents a significant advancement in the forecasting of stock prices, it also has its limitations. Certain internal and external factors that could influence stock prices were not taken into account. Despite these limitations, the study brought significant results and opens up further research opportunities for examining risk measurement, volatility of stock returns, and the formation of optimal portfolios on the Budapest Stock Exchange.

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Dr. Sándor Gáspár Assistant Professor,
Hungarian Agriculture and Life Science University, Insitute of Rural Development and Sustainable Economy

Dr. Gergő Thalmeiner Assistant Professor,
Hungarian Agriculture and Life Science University, Insitute of Rural Development and Sustainable Economy

Ákos Barta PhD student,
Hungarian Agriculture and Life Science University, Insitute of Rural Development and Sustainable Economy