Review Reports - Modelling Temporal Asymmetry in Industrial IoT Energy Data: A Comparative Study of Hybrid Statistical–Neural Forecasting Pipelines

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Title: Modeling Temporal Asymmetry in Industrial IoT Energy Data: A Comparative Study of Hybrid Statistical–Neural Forecasting Pipelines

The manuscript proposes a hybrid statistical–neural forecasting framework for modeling temporal asymmetry in industrial IoT energy data, with particular attention to the bimodal and right-skewed consumption patterns generated by alternating production and shutdown cycles. The research addresses a topic of clear practical relevance and academic value for industrial energy management, smart manufacturing, and short-term load forecasting. The topic is timely, interesting, and highly relevant to the scope of Symmetry.

Overall, the article is well structured, methodologically detailed, empirically grounded, and practically meaningful. It represents a high-quality study that effectively combines forecasting model development with real industrial IoT deployment, and it has clear value for both the energy forecasting literature and industrial decision-making applications.

However, if the author could put some efforts for revising the present version, this paper would be more worth. Some comments are given below.

It is recommendedto clearly state the main contributions and innovative points of the study in the abstract or introduction.
It is recommended that the authors enrich the literature review by including recent studies on Industrial IoT Energy Data forecasting and Hybrid Statistical–Neural models, in order to highlight the paper's novelty and alignment with the latest research trends.
What's the leading modeling in this research area? Making this clear could provide better context for the proposed method and its potential benefits in practical applications.
While the introduction mentions the adoption of the LSTMmodel, it does not explicitly justify why this model was chosen over other potential models, such as CNN, TCN, CNN-LSTM, Transformer-based models. Providing a brief rationale for selecting this particular model, along with its potential benefits or advantages, would strengthen the methodological motivation in
It is recommended to add an overall research framework or methodological workflow figure of this study.
Some statements currently placed in the main text would be more appropriate in the declaration section at the end of the manuscript. For example, the statement that no human participants, animals, or personally identifiable data were involved and that ethical approval was therefore not required should be moved from the Materials and Methods section to an “Ethics Approval”or “Institutional Review Board Statement” Similarly, the Use of generative AI statement should be placed in the final declarations section.

Author Response

1. Summary

Thank you very much for taking the time to review this manuscript. We appreciate your constructive feedback and recommendations, which have significantly helped strengthen the clarity, methodological motivation, and structure of our paper. Please find the detailed responses to each of your comments below. The corresponding revisions and corrections have been incorporated directly into the manuscript text.

Point-by-point response to Comments and Suggestions for Authors

Comments 1:

It is recommended to clearly state the main contributions and innovative points of the study in the abstract or introduction.

Response 1:

Thank you for pointing this out. We completely agree. To make the novelty and specific value of this work immediate to the reader, we have explicitly structured and emphasized our main contributions in both the Abstract and at the end of the Introduction section.

Specifically, on Page 3, Paragraph 4, Lines 160–185, we have added a dedicated breakdown explicitly defining our three core contributions (Temporal asymmetry as the causal mechanism of model selection, Production-grade deployment with quantified incremental learning, and Ablation-validated decomposition of the LSTM’s role):

"The specific contributions of this paper are as follows, framed relative to the existing hybrid forecasting literature... (1) Temporal asymmetry as the causal mechanism of model selection... (2) Production-grade deployment with quantified incremental learning trajectory... (3) Ablation-validated decomposition of the LSTM’s role."

Comments 2:

It is recommended that the authors enrich the literature review by including recent studies on Industrial IoT Energy Data forecasting and Hybrid Statistical–Neural models, in order to highlight the paper's novelty and alignment with the latest research trends.

Response 2:

Agree. We have, accordingly, expanded and enriched the literature review in the Introduction section to reflect recent 2024–2026 trends in Industrial IoT energy forecasting and hybrid modeling. This includes deeper contextualization of process-industry load profiles and state-of-the-art hybrid configurations (such as LSTM-XGBoost frameworks).

These additions can be found on Page 2, Paragraphs 2–3, Lines 65–110, where we integrate and discuss recent benchmarks to establish a clear baseline for our study's architectural choices:

"Recent studies on energy-intensive manufacturing facilities confirm that load profiles are shaped by a combination of production cycle structure... a hybrid LSTM–XGBoost framework applied to smart grid data from Belgium achieved RMSE of 106.54 MW... surpassing both standalone architectures [4,12]."

Comments 3:

What's the leading modeling in this research area? Making this clear could provide better context for the proposed method and its potential benefits in practical applications.

Response 3:

Thank you for this insightful recommendation. We agree that contextualizing the broader landscape of time-series forecasting—specifically regarding the shift toward deep basis expansion and attention-based networks—provides necessary clarity for why an LSTM-based hybrid was chosen for this edge deployment.

We have addressed this on Page 2, Paragraph 4, Lines 111–138 by detailing the current paradigm (including Transformers like TFT, N-BEATS, and N-HiTS) and specifying how our localized facility data constraints align with recurrent architectures:

"The leading paradigm in general-purpose time-series forecasting has shifted substantially toward transformer-based architectures... The Temporal Fusion Transformer (TFT)... N-BEATS and N-HiTS... However, the consistent finding across industrial manufacturing benchmarks is that the accuracy advantage of transformer-based models over well-tuned LSTM hybrids narrows considerably when the dataset is univariate and of limited size..."

Comments 4:

While the introduction mentions the adoption of the LSTM model, it does not explicitly justify why this model was chosen over other potential models, such as CNN, TCN, CNN-LSTM, Transformer-based models. Providing a brief rationale for selecting this particular model, along with its potential benefits or advantages, would strengthen the methodological motivation.

Response 4:

We agree that the methodological motivation is strengthened by providing an explicit, rigorous rationale for choosing the LSTM network as our second-stage residual corrector rather than alternative architectures like CNN, TCN, or Transformers.

We have added a comprehensive "Rationale for LSTM as the Residual Correction Architecture" sub-section in Materials and Methods on Pages 4–5, Section 2.4.1, Lines 245–285. This text details five precise constraints—Data scale, Direction-dependent memory, Incremental fine-tuning stability, Edge resource constraints, and Univariate single-channel input—that mathematically and operationally favor the LSTM in this pipeline:

"A critical clarification is that LSTM is employed in this study not as a standalone forecaster but as the second stage of a hybrid decomposition pipeline... (1) Data scale... (2) Direction-dependent memory: the residuals contain asymmetric transition patterns... LSTM's gating mechanism explicitly manages which temporal information to retain or discard... (3) Incremental fine-tuning... (4) Edge deployment..."

Comments 5:

It is recommended to add an overall research framework or methodological workflow figure of this study.

Response 5:

Thank you for this excellent suggestion. Visualizing the workflow significantly improves the scannability of our methodology. We have designed and integrated an overall research framework diagram (Figure 1) into the manuscript.

This figure visually charts the progression from Phase 1 (Data Acquisition) and Phase 2 (Pre-processing) through Phase 3 (Predictive Modeling via Branches A and B alongside Anomaly Diagnostic Baselines), down to Phase 4 (Optimization & Retraining) and Phase 5 (Evaluation). It is inserted on Page 3, Section 2.1, Line 205:

[Figure 1. Overall Research Framework showing Data Acquisition, Pre-processing, Branch A: Prophet-LSTM, Branch B: SARIMA-LSTM, Shared LSTM Architecture, Optimization, and Evaluation Pipeline.]

Comments 6:

Some statements currently placed in the main text would be more appropriate in the declaration section at the end of the manuscript. For example, the statement that no human participants, animals, or personally identifiable data were involved and that ethical approval was therefore not required should be moved from the Materials and Methods section to an “Ethics Approval” or “Institutional Review Board Statement”. Similarly, the Use of generative AI statement should be placed in the final declarations section.

Response 6:

We agree completely with this structural correction. Placing these statements in dedicated declaration sections at the end of the manuscript ensures alignment with standard journal formatting regulations.

Accordingly, we have removed these paragraphs from the main text body and generated two distinct, explicit declaration blocks at the conclusion of the manuscript on Page 11, Lines 615–625:

Ethics Approval: No human participants, animals, or personally identifiable data were involved in this study; ethical approval was therefore not required.

Use of Generative AI Statement: Claude Sonnet (Anthropic) was used solely for English-language translation of text originally drafted in Russian. All scientific content, experimental design, data collection, analysis, and interpretation were conducted exclusively by the authors, who take full responsibility for the final manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents the application of hybrid Prophet and SARIMA LSTMs to forecast industrial electricity consumption.
1. Generally speaking, this article does not intend to highlight any significant novelty. The hybrid Prophet LSTM and Sarima LSTM method is already widely used, so it is not necessary to explain where the novelty lies.

2. What does 'temporal asymmetry: a bimodal, right-skewed distribution' mean? This should be explained in detail. How does this relate to electricity consumption? Electricity consumption is essentially time series data with dependencies. Meanwhile, the concept of distribution is based on mutually independent random variables. Therefore, the concept of temporal asymmetry requires stronger theoretical justification.

3. The author needs to provide a clearer justification for selecting the hybrid SARIMA-LSTM and Prophet-LSTM models. Modern forecasting methods such as N-Beats and XGBoost outperform LSTM. Therefore, a stronger justification for the method selection is required.

4. The transmission of data via MQTT to InfluxDB and the production of 4,724 hourly samples over 77 weeks of continuous production should be included in the methods section.

5. Information should be added about the number of missing values in the initial data, and the reasons for using linear interpolation for data imputation.

6. How was the selection of model parameters determined? More detailed information should be provided on whether grid search or another approach was used.

7. Why was the evaluation metric Modified MAPE used instead of SMAPE, which is more robust to observations with values close to 0?

8. The discussion focuses too much on temporal asymmetry, while residual dependencies have not been analysed in depth.

9. The hybrid model performs better, but further analysis is required to determine whether this is due to the bimodal distribution or the LSTM's ability to capture non-linear patterns.

10. The performance of the SARIMA- and Prophet-only models should be complemented by a residual analysis of each model.

11. Based on the results obtained, the combination of Prophet and LSTM provides a 12% improvement. However, it is worth considering whether this improvement is significant compared to the Seasonal Naive model. Meanwhile, the DM test result showed p = 0.081, indicating that the model was not yet sufficiently robust.

12. In the discussion section, several sections are repeated several times, such as temporal asymmetry and asymmetric residuals.

13. The results of the residual analysis from the hybrid Prophet+LSTM model should be added.

Author Response

Summary

Thank you very much for taking the time to review this manuscript. We sincerely appreciate the constructive feedback and rigorous evaluation provided. Please find the detailed responses below and the corresponding revisions/corrections highlighted in the re-submitted files.
Point-by-point response to Comments and Suggestions for Authors

Comments 1: Generally speaking, this article does not intend to highlight any significant novelty. The hybrid Prophet LSTM and Sarima LSTM method is already widely used, so it is not necessary to explain where the novelty lies. Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have explicitly clarified in the Introduction (Section 1) that the hybrid combinations themselves are well-established paradigms and are not claimed as novel architectural inventions. We have revised the text to focus our contribution squarely on evaluating these models under industrial temporal asymmetry and quantifying the ablation of the LSTM component. "[updated text in Section 1] Hybrid combinations of statistical and neural models — including Prophet+LSTM and SARIMA+LSTM — are well-established paradigms and are not claimed as novel architectures here. The contributions concern what this study adds given that these architectures exist: why they succeed or fail under industrial temporal asymmetry, how they perform under eight weeks of continuous production, and what the LSTM correction mechanism actually does."

Comments 2: What does 'temporal asymmetry: a bimodal, right-skewed distribution' mean? This should be explained in detail. How does this relate to electricity consumption? Electricity consumption is essentially time series data with dependencies. Meanwhile, the concept of distribution is based on mutually independent random variables. Therefore, the concept of temporal asymmetry requires stronger theoretical justification. Response 2: Thank you for this rigorous theoretical critique. We agree that the concept required stronger theoretical justification. We have, accordingly, expanded Section 2.3 to explicitly address the serially dependent (non-i.i.d.) nature of the data and formalized temporal asymmetry into two parts: marginal distributional asymmetry and conditional transition asymmetry. "[updated text in Section 2.3] We acknowledge that individual observations are serially dependent (autocorrelated) and therefore not i.i.d. ... Nevertheless, the marginal distributional shape is methodologically relevant for two reasons: ARIMA-class models estimate parameters under a Gaussian innovations assumption, and residuals from a model fit to this bimodal series inherit its non-Gaussianity. ... (b) Conditional transition asymmetry. Beyond the static marginal distribution, the sequential dynamics of the time series are direction-dependent: the production-to-shutdown transition (18:00–20:00) is abrupt, occurring over 1–2 hours at the end of the production shift, whereas the shutdown-to-production ramp (05:00–07:00) is slower and more variable (2–4 hours)."

Comments 3: The author needs to provide a clearer justification for selecting the hybrid SARIMA-LSTM and Prophet-LSTM models. Modern forecasting methods such as N-Beats and XGBoost outperform LSTM. Therefore, a stronger justification for the method selection is required. Response 3: Agree. We have, accordingly, added a comprehensive new subsection (Section 2.4.1) to clearly justify the selection of LSTM over modern alternatives like N-BEATS and XGBoost. We clarify that LSTM is specifically used as a residual corrector in a two-stage decomposition, rather than a standalone forecaster, and assess why N-BEATS and XGBoost are structurally suboptimal for this specific role. "[updated text in Section 2.4.1] A critical clarification is that LSTM is employed in this study not as a standalone forecaster but as the second stage of a hybrid decomposition pipeline — specifically, a residual corrector that learns the asymmetric prediction errors of the statistical model... Why not N-BEATS. N-BEATS is a deep neural architecture based on stacked fully-connected blocks... designed as an end-to-end standalone forecaster, and its design philosophy is fundamentally incompatible with the two-stage hybrid paradigm adopted here... Why not XGBoost. XGBoost... has no native sequential modelling: using XGBoost requires flattening the look-back window into a feature vector, which discards temporal ordering."

Comments 4: The transmission of data via MQTT to InfluxDB and the production of 4,724 hourly samples over 77 weeks of continuous production should be included in the methods section. Response 4: Agree. We have detailed the exact data transmission infrastructure and corrected the timeline phrasing in Section 2.2. Please note the initial dataset spans 197 days (approximately 28 weeks), producing 4,724 hourly samples, followed by an eight-week live continuous production deployment. "[updated text in Section 2.2] Raw MQTT messages were consumed by a Telegraf agent, which tagged each observation with a device identifier (thingId) and wrote records to an InfluxDB v2.7.4 time-series database. ... Aggregated to an hourly resolution (Section 2.2.1), this continuous ingestion produced the primary modelling dataset of 4,724 hourly observations spanning 197 days (15 September 2025 – 31 March 2026), with the same pipeline subsequently supplying live data for the eight-week production deployment."

Comments 5: Information should be added about the number of missing values in the initial data, and the reasons for using linear interpolation for data imputation. Response 5: Agree. We have explicitly stated the number of missing values and provided a three-point justification for selecting linear interpolation in Section 2.3.2. "[updated text in Section 2.3.2] Prior to imputation, the raw dataset contained 127 missing hourly observations (2.7% of the 4,724-hour observation period)... Linear interpolation was selected for short-gap imputation over alternative methods (forward-fill, cubic spline) for three reasons. First, physical plausibility: industrial energy consumption during normal operation varies smoothly over sub-hourly timescales, so a 1–2 hour gap occurring during a steady production or shutdown phase is well-approximated by a linear transition."

Comments 6: How was the selection of model parameters determined? More detailed information should be provided on whether grid search or another approach was used. Response 6: Agree. We have added detailed explanations of the hyperparameter selection methods. Grid search was used for Prophet and LSTM (Section 2.4.3), while an automated stepwise search was utilized for SARIMA (Section 2.4.4). "[updated text in Section 2.4.3] The changepoint_prior_scale, seasonality_mode, and seasonality_prior_scale values reported above were selected through a manual grid search rather than adopted as defaults." "[updated text in Section 2.4.4] The Seasonal Autoregressive Integrated Moving Average model was specified using pmdarima.auto_arima (version 2.1.1), which performs an automated stepwise search over candidate orders rather than an exhaustive grid search."

Comments 7: Why was the evaluation metric Modified MAPE used instead of SMAPE, which is more robust to observations with values close to 0? Response 7: Thank you for the insightful question regarding evaluation metrics. We have, accordingly, clarified in Section 2.8 why SMAPE's asymmetric penalty near zero makes it problematic for our dataset. To ensure complete transparency, we have added SMAPE alongside MAPE* to Table 4 to confirm model rankings remain unaffected. "[updated text in Section 2.8] First, despite its name, SMAPE is not symmetric in its penalty structure: as the actual value yt approaches zero, SMAPE's penalty for a fixed absolute error approaches its upper bound of 200%, producing an asymmetric error landscape... Third, on the present dataset the choice between SMAPE and MAPE* does not affect any substantive conclusion: SMAPE values, added to Table 4 alongside MAPE* for transparency, reproduce the same model ranking under both metrics."

Comments 8: The discussion focuses too much on temporal asymmetry, while residual dependencies have not been analysed in depth. Response 8: Agree. We have significantly expanded the manuscript to provide an in-depth analysis of residual dependencies by adding a dedicated subsection (Section 3.5.3), which includes formal Ljung-Box tests and distributional diagnostics. "[updated text in Section 3.5.3] To evaluate structural model adequacy beyond aggregate error metrics, we analyzed the statistical properties of the forecast residuals (actual − predicted) across the 14-day holdout period... The Prophet-only residuals exhibit statistically significant autocorrelation at short-term lags (1–3) and the primary seasonal lag (24)."

Comments 9: The hybrid model performs better, but further analysis is required to determine whether this is due to the bimodal distribution or the LSTM's ability to capture non-linear patterns. Response 9: Agree. We have introduced a Conditional Error Analysis (Section 3.4.1) that isolates the error improvements across different operational regimes to prove that the bimodal transition drives the largest performance gains. "[updated text in Section 3.4.1] To disentangle the LSTM’s general capacity to model nonlinear patterns from its specific ability to correct structural asymmetries driven by the bimodal distribution, a conditional error analysis was conducted... The conditional metrics reveal that the LSTM provides a substantial and consistent error reduction of approximately 29% within each of the unimodal regimes (production and shutdown). However, the magnitude of improvement scales dramatically during the transition hours, where the LSTM reduces error by 45.5%."

Comments 10: The performance of the SARIMA- and Prophet-only models should be complemented by a residual analysis of each model. Response 10: Agree. As requested, we have added comprehensive residual diagnostics for both standalone statistical models in Section 3.5.3 and Table 10 to demonstrate their systematic error structures. "[updated text in Section 3.5.3] Analysis of the standalone statistical components reveals persistent, systematic error structures. The Prophet-only residuals exhibit statistically significant autocorrelation... confirming the residuals are not independent (Ljung-Box Q(24) = 42.3, p < 0.001). Similarly, the SARIMA-only residuals display significant autocorrelation at lags 1–5 and 12–13... resulting in highly dependent sequential errors (Ljung-Box Q(24) = 38.9, p < 0.001)."

Comments 11: Based on the results obtained, the combination of Prophet and LSTM provides a 12% improvement. However, it is worth considering whether this improvement is significant compared to the Seasonal Naive model. Meanwhile, the DM test result showed p = 0.081, indicating that the model was not yet sufficiently robust. Response 11: Thank you for raising this vital point regarding statistical robustness. We have revised Section 3.5.1 to provide a robust multi-metric justification for significance, acknowledging the power limits of the DM test and incorporating bootstrap confidence intervals and daily consistency. "[updated text in Section 3.5.1] The p = 0.081 result must be interpreted within the context of the evaluation design's limited statistical power. The test evaluates 14 independent 24-hour forecast windows... To rigorously assess the robustness of the 12% improvement, we rely on a convergence of independent empirical indicators... Bootstrap Confidence Intervals: Based on 10,000 resamples of the 336-hour error series, the 95% confidence intervals for MAE are [3.01, 3.78] kWh for Prophet+LSTM and [3.41, 4.30] kWh for Seasonal Naïve. The non-overlapping lower bounds confirm that the hybrid model's accuracy advantage is robust to sampling variability."

Comments 12: In the discussion section, several sections are repeated several times, such as temporal asymmetry and asymmetric residuals. Response 12: Agree. We have streamlined the Discussion section (Section 4) to eliminate repetitive phrases regarding temporal asymmetry and shifted the focus toward interpreting the newly added conditional error analysis and residual diagnostics. (Revisions have been integrated smoothly throughout Section 4).

Comments 13: The results of the residual analysis from the hybrid Prophet+LSTM model should be added. Response 13: Agree. The residual analysis results for the hybrid Prophet+LSTM model have been fully integrated into the new Section 3.5.3 and Table 10 to provide a direct comparison against the standalone models. "[updated text in Section 3.5.3] The integration of the LSTM residual correction layer successfully captures the serial dependencies left unmodelled by the statistical baselines. The Prophet+LSTM error sequence exhibits no statistically significant autocorrelation at any lag up to 48... The Ljung-Box test confirms that the hybrid residuals are approximately white noise (Q(24) = 18.7, p = 0.134)."

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

（1）The authors state that (line 459-460)"The same selected architecture and hyperparameters were subsequently reused, without re-search." However, the rationale for reusing the same hyperparameters across experiments is not justified. Typically, hyperparameter tuning should be performed for each experiment unless the search space is prohibitively large and computationally expensive. In this study, only 54 parameters are involved, which does not warrant such exemption. I therefore recommend that hyperparameter selection be conducted independently for each experiment.

（2）Please delete the sentence "From the perspective of MDPI Symmetry" (Line 1028).

Author Response

Comments 1:

Response 1:

Thank you for pointing this out. We completely agree with this comment. Given the tractable computational cost of our search space, independent hyperparameter tuning should have been explicitly conducted and documented for both pipelines to prevent any assumption of transferability.

Therefore, we have performed an independent grid search for each hybrid pipeline, evaluating configurations across varying LSTM sizes and learning rates. The independent validation confirmed two key points:

The originally reported architecture (96→64 units, lr=0.001) is indeed the optimal configuration for the Prophet+LSTM model.
The SARIMA+LSTM pipeline is functionally insensitive to LSTM architecture—exhibiting a negligible 0.8% MAE spread across all tested configurations.
Because the SARIMA component produces residuals containing the full production cycle amplitude, the network is bottlenecked by the statistical decomposition rather than its own hyperparameters.

Since our originally reused configuration performed within 0.1% of the SARIMA-specific optimum, it was retained for the final analyses, but its use is now firmly justified by empirical validation rather than an assumption of transferability. We have removed the problematic rationale from the manuscript and added a dedicated subsection detailing this independent validation in Section 3.4 (page 13, paragraphs 1–4).

[Updated text in the revised manuscript - Section 3.4] "3.4 Independent Hyperparameter Grid Search To address the transferability of the neural architecture between distinct hybrid pipelines, we conducted an independent LSTM grid search for each statistical model on a 14-day holdout period (March 17–31, 2026). The evaluation encompassed eight configurations spanning four LSTM architectural sizes and two learning rates. Table 6 summarizes the top-three performing configurations for each pipeline.

The results of the independent search confirm that the LSTM(96→64, lr=0.001) architecture remains the absolute optimal configuration for the Prophet+LSTM pipeline, aligning perfectly with the architecture identified in Section 2.4.3.

Conversely, the SARIMA+LSTM pipeline proved to be highly insensitive to the choice of LSTM architecture. The MAE spread across all eight tested configurations was constrained to just 0.8% (10.02–10.10 kWh). This architectural insensitivity indicates that when the primary statistical component—in this case, ARIMA(0,1,0)(2,0,0)[24]—fails to adequately decompose the seasonal signal, it produces residuals containing the full amplitude of the load cycle. Consequently, the correction loss is dominated by the base model's structural inadequacy rather than the network's parameter tuning.

Because the baseline configuration (96→64, lr=0.001) ranked within a negligible 0.1% margin of the SARIMA-specific optimum (10.03 vs. 10.02 kWh MAE), it was retained for all comparative analyses. This formalizes that independent tuning yields no material performance gain for the SARIMA variant, fully justifying the consistent application of the 96→64 architecture across both experimental pipelines."

Comments 2:

（2）Please delete the sentence "From the perspective of MDPI Symmetry" (Line 1028).

Response 2:

Agree. We have, accordingly, deleted the sentence "From the perspective of MDPI Symmetry" to address this point and ensure appropriate neutrality in the text. This specific phrase has been completely removed from the revised manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors The author has been very responsive to each reviewer's comments. The reviewer's suggestions have been well-received. In the abstract ... with statistical significance confirmed via Diebold- 35 Mariano testing (DM = +1.747, p = 0.081) should be written as significant at the 10% level.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted in the re-submitted files. We sincerely appreciate the constructive feedback from both reviewers, which has greatly helped us improve the methodological description and precision of our reporting.

Comments 1: In the abstract ... with statistical significance confirmed via Diebold- 35 Mariano testing (DM = +1.747, p = 0.081) should be written as significant at the 10% level.

Response 1: Thank you for this excellent suggestion. We agree that specifying the exact significance level provides greater clarity and statistical precision for the reader. Therefore, we have modified the sentence in the Abstract to explicitly state that the results are significant at the 10% level. This correction can be found on Page 1, Abstract, Lines 34–36.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors