Estimating Volatility of Saudi Stock Market Using Hybrid Dynamic Evolving Neural Fuzzy Inference System Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is professionally written and provides valuable insights into the volatility estimation of the Saudi stock market using a novel hybrid model combining MODWT and DENFIS. The authors have conducted a thorough analysis and the results are promising, indicating that this model can be a useful tool for investors and policymakers.

However, as an academic and practicing quant, I have a concern regarding the measurement of risk or deviation without considering the signal-to-noise ratio, such as the Sharpe ratio. Estimating volatility alone can be one-sided; it is important to evaluate how much of the volatility is attributable to the actual market signal versus noise. If the volatility is relatively small but the mean return is ten times smaller, that small volatility means nothing in assessing the portfolio returns.

I suggest the authors read the following references and comment on how their results can be extended to encompass estimates of reward-risk ratios:

• Princeton University Library - OAR: Reward to Risk Ratio,https://oar.princeton.edu/handle/88435/pr1tz9b
• Journal of Investment Strategies: Reward-Risk Ratios,https://www.risk.net/journal-investment-strategies/2317310/reward-risk-ratios

Despite this concern, the paper deserves publication due to its methodological rigor and the potential practical applications of the proposed model.

Author Response

Dear professor,

 

we wanted to express our heartfelt gratitude for your invaluable contribution as the reviewer of our work. Your thorough evaluation of our methodology, results, and conclusions has undoubtedly enhanced the rigor and validity of our study. We genuinely appreciate the time and effort you invested in carefully reviewing our manuscript.

 

** Comments 1: However, as an academic and practicing quant, I have a concern regarding the measurement of risk or deviation without considering the signal-to-noise ratio, such as the Sharpe ratio. Estimating volatility alone can be one-sided; it is important to evaluate how much of the volatility is attributable to the actual market signal versus noise. If the volatility is relatively small but the mean return

is ten times smaller, that small volatility means nothing in assessing the portfolio returns.

 

Authors’ response:

 

Thank you for your insightful comments and concerns. In our study focusing on the Saudi stock market characterized by significant volatility, we acknowledge the importance of evaluating risk beyond mere estimation of volatility. To address this, we have implemented the Maximal Overlap Discrete Wavelet Transform (MODWT) as a data filter. The MODWT enables us to segregate the data into detailed components (outliers) and approximation data (without outliers). Subsequently, we focus on the smoothed part of the data after removing the detailed components, ensuring that we consider the significant movements in this market. Given the substantial volatility in this context, our methodology aims to capture and analyze the market dynamics effectively, taking into account both the market signal and noise to provide a more comprehensive assessment of close prices. In future work, we will incorporate metrics such as the Sharpe ratio and signal-to-noise ratio to further enhance our risk evaluation strategies.

 

 

** 2:  I suggest the authors read the following references and comment on how their results can be extended to encompass estimates of

reward-risk ratios: Princeton University Library - OAR: Reward to Risk Ratio,https://oar.princeton.edu/handle/88435/pr1tz9b

Journal of Investment Strategies: Reward-Risk

Ratios,https://www.risk.net/journal-investment

strategies/2317310/reward-risk-ratios

 

Authors’ response:

 

Thank you for recommending these insightful references. We appreciate your guidance, and these papers will undoubtedly serve as valuable resources for expanding our research to encompass estimates of reward-risk ratios in future studies. By delving into these references and considering how their results can be applied to our work, we aim to enhance the depth and robustness of our analysis, incorporating reward-risk ratios to provide a more comprehensive evaluation of the investment landscape. Your input is invaluable in shaping the direction and scope of our future research, and we are grateful for your recommendations.

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This study is interesting because it combines a dynamically evolving fuzzy neural inference system (DENFIS) and a nonlinear spectral model, maximum overlap discrete wavelet transform (MODWT). Therefore, the study should focus only on the development of DENFIS and MODWT models in estimating stock market volatility. It is more strange to present the estimation of the panel data regression method with three modes: OLS, fixed, and random, which are not shown in the mathematical model and research methodology.

 

·         The title of the article is not "Volatility of Financial Saudi Stock Market"; it should be changed to "Volatility of Saudi Stock Market" (lines 2-3)

·         Several theories revealed in the literature review section must be more appropriate to explain stock market volatility, including behavioral theories (line 247). The study does not mention all aspects related to behavior in stock market volatility

·         Mathematical Models (lines 313-543) should be part of the research methods, and the relationship between the specifications of the developed model and its testing should be clearly presented. The Research Design and Methodology section also presents the research results that should be included in the research results section.

·         What is the purpose of estimating the panel data model (line 767), and how is it related to the mathematical model developed?

·         The Results and Discussion section has yet to be widely disclosed, especially in-depth discussions of empirical findings.

·         Conclusions are more concisely related to the main findings of the research, and the results of statistical testing are not further interpreted.

·         References are inadequate and need to be added to support the proper literature related to the theoretical underpinning of stock market volatility.

Comments for author File: Comments.docx

Author Response

Dear professor,

 

we wanted to express our heartfelt gratitude for your invaluable contribution as the reviewer of our work. Your thorough evaluation of our methodology, results, and conclusions has undoubtedly enhanced the rigor and validity of our study. We genuinely appreciate the time and effort you invested in carefully reviewing our manuscript.

 

 Comments 1- the study should focus only on the development of DENFIS and MODWT models in estimating stock market volatility. It is more strange to present the estimation of the panel data regression method with three modes: OLS, fixed, and random, which are not shown in the mathematical model and research methodology

 

 

Authors’ response:

 

Thank you for your feedback on our paper.  the following paragraph added to Section 3 (Research Design and Mathematical Models)

“Four, in the process of selecting input variables (LCP, Loil, LCL, and IB), various statistical tests are employed. The AC test assesses whether past values influence current values, while the PAC test identifies direct relationships between variables while controlling for intervening variables. Correlation analysis evaluates the relationships between input variables to avoid multicollinearity, whereas Granger Causality tests determine predictive relationships between variables. OLS regression optimizes the model fit, and fixed effects models control for time-invariant factors, with random effects models capturing general unobserved heterogeneity across panel units. In fixed and random effects models, time series data is transformed into panel data using years to observe how input variables impact the output variable over time. Selecting relevant input variables effectively enhances the accuracy and reliability of the model selection process, providing valuable insights into the relationships between predictors and the outcome variable across different time periods.”

 

 

 

** 2- Several theories revealed in the literature review section must be more appropriate to explain stock market volatility, including behavioral theories (line 247).

 

 

 

 

Authors’ response:

 

Thank you for your comments and valuable insights. We have taken your feedback into consideration and revised our literature review accordingly. Our literature review  delves into theories starting from the Efficient Market Hypothesis (EMH) introduced by Fama in 1970, extending to current discussions that elucidate the behavior of volatility in the stock market. Furthermore, we have included an exploration of the variables that could potentially contribute to volatility behaviors. With these enhancements, we believe that our literature review adequately addresses the range of theories and variables pertinent to understanding stock market volatility. We appreciate your feedback. we add new paragraph in literature review section

“The factors influence the dynamics of financial markets. Investor sentiment, characterized by the emotions and attitudes of market participants, stands out as a significant driver of market volatility. Market psychology, which delves into collective behavioral patterns such as herd mentality, underscores the importance of understanding the human element in market movements. External factors like economic indicators, geopolitical events, and regulatory changes also play a crucial role in shaping stock market volatility. Regulatory environments, market liquidity, and information dissemination further contribute to the intricate web of influences on market behavior and volatility, highlighting the multifaceted nature of financial markets (Aouadi et al. 2013, Gavrilakis et al. 2024, Vo and Phan 2019).“

 

 

** 3- Mathematical Models (lines 313-543) should be part of the

research methods, and the relationship between the specifications of the developed model and its testing should be clearly presented. The Research Design and Methodology section also presents the research results that should be included in the research results section.

 

 

Authors’ response:

 

Thank you for your insightful comments. We have carefully addressed your suggestions regarding the inclusion of Mathematical Models in the research methods section and include research design, ensuring a clear presentation of the relationship between the model specifications and its testing. Additionally, we have integrated the research design and results and methodology details with the research results, as you recommended. By incorporating these adjustments into sections 3 and 4, we have aimed to enhance the clarity and coherence of our research presentation. Your feedback has been invaluable in refining our work, and we appreciate your guidance.

 

 

** 4 - What is the purpose of estimating the panel data model (line 767), and how is it related to the mathematical model developed?

 

 

Authors’ response:

Thanks for your inquiry about the purpose of estimating the panel data model. We elaborate on this in Section 3, where we outline that through OLS regression, the model fit is optimized, while fixed effects models aid in controlling for time-invariant factors and random effects models capture general unobserved heterogeneity across panel units. Notably, the transformation of time series data into panel data using years allows us to observe how input variables influence the output variable over years. This selection process of pertinent input variables enhances both the accuracy and reliability of our model, offering valuable insights into the relationships between predictors and the outcome variable across various time periods.

 

 

                                                        

** 5- The Results and Discussion section has yet to be widely disclosed, especially in-depth discussions of empirical findings

 

Authors’ response:

 

Thank you for your insightful feedback. Regarding the Results and Discussion section, we have extensively addressed your concerns. In Section 4 of our work, spanning from page 15 to 23, we meticulously present the new hybrid model and engage in detailed discussions about the empirical findings. Through this thorough analysis, we aim to provide a comprehensive understanding of the results, fostering a deeper insight into our research outcomes. Your comments have been instrumental in guiding our approach, and we appreciate your input.

 

** 6-   Conclusions are more concisely related to the main findings of the research, and the results of statistical testing are not further interpreted.

 

 

Authors’ response:

Thank you for your valuable feedback. We have carefully considered your suggestions and made the necessary adjustments. By removing the statistical numbers, we aim to enhance the conciseness of our conclusions, ensuring a more direct connection to the main findings of the research. Additionally, we have worked on providing more insightful interpretations of the results of statistical testing, bridging the gap between the empirical data and the overarching implications of our study. Your comments have been pivotal in refining our work, and we appreciate your guidance in strengthening the clarity and impact of our conclusions.

 

 

** 7- References are inadequate and need to be added to support the proper literature related to the theoretical underpinning of stock market volatility

 

Authors’ response:

 

Thank you for your feedback. We have taken note of your suggestion regarding the adequacy of references to support the theoretical underpinning of stock market volatility. We have made update to our literature review to ensure that it is well-supported by a comprehensive range of references that align with the theoretical framework of our research. By incorporating additional relevant sources, we aim to strengthen the foundation of our study and provide a more robust theoretical context for understanding stock market volatility. Your input has been invaluable in refining our work, and we appreciate your guidance in enhancing the quality of our references.

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Panel data regression methods have been presented in Research Design and Mathematical Models. However, its relationship with the models developed from the dynamically evolving fuzzy neural inference system (DENFIS) and the nonlinear spectral model, maximum overlap discrete wavelet transform (MODWT), must be clarified. The literature review focuses more on financial behavior, such as investor sentiment, which is characterized by the emotions and attitudes of market players. Market psychology, which investigates collective behavioral patterns such as herd mentality and fear of missing out (FOMO), underlines the importance of understanding the human element in market movements. Investor behavioral aspects should be included in the DENFI and MODWT modeling to estimate the volatility of the Saudi stock market. It would be better if this study also added a qualitative analysis of investor behavior.

Author Response

Dear professor,

 

we wanted to express our heartfelt gratitude for your invaluable contribution as the reviewer of our work. Your expertise, meticulous attention to detail, and insightful feedback have played a crucial role in shaping our paper and improving its quality. Your constructive criticism and suggestions have challenged us to think deeper, and present our research in a more coherent and impactful manner. Your thorough evaluation of our methodology, results, and conclusions has undoubtedly enhanced the rigor and validity of our study. We genuinely appreciate the time and effort you invested in carefully reviewing our manuscript.

 

 

 

 The literature review focuses more on financial behavior, such as investor sentiment, which is characterized by the emotions and attitudes of market players. Market psychology, which investigates collective behavioral patterns such as herd mentality and fear of missing out (FOMO), underlines the importance of understanding the human element in market movements. Investor behavioral aspects should be included in the DENFI and MODWT modeling to estimate the volatility of the Saudi stock market. It would be better if this study also added a qualitative analysis of investor behavior.

 

**Reveiwer Question-1: Panel data regression methods have been presented in Research Design and Mathematical Models. However, its relationship with the models developed from the dynamically evolving fuzzy neural inference system (DENFIS) and the nonlinear spectral model, maximum overlap discrete wavelet transform (MODWT), must be clarified.

 

 

Authors’ response:

 

Thank you for your feedback on our paper.  the following paragraph added to Section 3 (Research Design and Mathematical Models)

“

In fixed and random effects models, time series data is transformed into panel data using years to observe how input variables impact the output variable over time. To enhance the predictive capabilities of our models, we intend to amalgamate the selected input variables with the approximate coefficient component extracted from the MODWT model into the DENFIS model, which encompasses both the input variables and the output variable. This integration strategy aims to harness the synergies between these methodologies to improve the precision and robustness of our output variable predictions.

“

 

 

**Reveiwer Question-2:  The literature review focuses more on financial behavior, such as investor sentiment, which is characterized by the emotions and attitudes of market players. Market psychology, which investigates collective behavioral patterns such as herd mentality and fear of missing out (FOMO), underlines the importance of understanding the human element in market movements. Investor behavioral aspects should be included in the DENFI and MODWT modeling to estimate the volatility of the Saudi stock market. It would be better if this study also added a qualitative analysis of investor behavior.

 

 

 

Authors’ response:

 

Thank you for your feedback. We add the following in the literature review:

 

“The factors influence the dynamics of financial markets. Investor sentiment, characterized by the emotions and attitudes of market participants, stands out as a significant driver of market volatility. Market psychology, which delves into collective behavioral patterns such as herd mentality and fear of missing out (FOMO), underscores the importance of understanding the human element in market movements. External factors like economic indicators, geopolitical events, and regulatory changes also play a crucial role in shaping stock market volatility. Regulatory environments, market liquidity, and information dissemination further contribute to the intricate web of influences on market behavior and volatility, highlighting the multifaceted nature of financial markets (Aouadi et al. 2013, Gavrilakis et al. 2024, Vo and Phan 2019). Stock price volatility mirrors investor behavior by reflecting their collective emotions, decisions, and sentiments during turbulent market periods. Heightened volatility often amplifies investor actions driven by fear, greed, and uncertainty, leading to rapid buying or selling trends that intensify market fluctuations. The MODWT models, acting as filters to distinguish detailed (non-smooth or high frequency) and approximate (smooth) data, will help identify outliers in investor behavior and focus on the smoother data for market analysis. Subsequently, the DENFIS model incorporates the output variable (smooth data from MODWT) in conjunction with input variables to forecast stock market volatility.”

 

In addition, Thank you for your valuable feedback regarding the inclusion of investor behavioral aspects in the DENFI and MODWT modeling to enhance the estimation of volatility in the Saudi stock market. We appreciate your recommendation, and we acknowledge the importance of delving deeper into the qualitative aspects of investor behavior to gain a more comprehensive understanding of market dynamics.

 

In our future work, we will include a qualitative analysis of investor behavior to further enrich our study and provide a holistic view of the factors influencing stock market volatility. By integrating qualitative insights into our modeling approach, we aim to capture the nuances of investor sentiment, emotions, and decision-making processes more effectively.

Author Response File: Author Response.docx