A Comparative Study of Univariate Models for Baltic Dry Index Forecasting

Round 1

Reviewer 1 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

The manuscript file has been modified, but there are still errors (duplicate information in Table 1 and Figure 3), which, as I recall, were pointed out in the original review. The authors responded to this suggestion: "We acknowledge that Table 1 and Figure 2 currently contain overlapping information. To address this, we have added Table 2 (pp. 15-16, line 533) to present descriptive statistics (mean, median, standard deviation, skewness, kurtosis, minimum, and maximum) of the data series." Why wasn't Table 1 removed?
I appreciate the authors' contribution to improving the article, but I don't fully understand their approach. The original article was highly technical. The authors attempted to make it more accessible to the average reader, but the results are vary. Atuhors, when pointing out potential added value or limitations, they should not address purely mathematical (econometrics) aspects in time series analysis but economic ones, which anyone reading it will understand.

Author Response

Response to Reviewer 1

We sincerely thank the reviewer for the thoughtful and detailed comments that have significantly improved the quality and clarity of our paper. Below we address each point carefully and describe the corresponding revisions.

1. The manuscript file has been modified, but there are still errors (duplicate information in Table 1 and Figure 3), which, as I recall, were pointed out in the original review. The authors responded to this suggestion: "We acknowledge that Table 1 and Figure 2 currently contain overlapping information. To address this, we have added Table 2 (pp. 15-16, line 533) to present descriptive statistics (mean, median, standard deviation, skewness, kurtosis, minimum, and maximum) of the data series." Why wasn't Table 1 removed?

Response:

We thank the reviewer for this comment and apologize for any confusion caused in the previous revision. Table 1 was intentionally retained because it reports the original BDI data used in the empirical analysis, thereby ensuring transparency, reproducibility, and verifiability of the results. Presenting the raw data allows other researchers to replicate the study and independently validate the findings.

Figure 3 complements Table 1 by illustrating the evolution of the monthly BDI series and visually indicating a clear trend and potential nonstationary. This naturally motivates the subsequent stationary analysis, leading to the statement that “this observation is confirmed by the Augmented Dickey–Fuller (ADF) test,” and supports a logical progression from data presentation to statistical testing.

 

2. The original article was highly technical. The authors attempted to make it more accessible, but the results vary. When pointing out added value or limitations, the authors should focus on economic rather than purely mathematical aspects.

Response:

We greatly appreciate this insightful suggestion. In response to this comment, we have revised the limitations and future research to emphasize economic and market-related limitations, including structural changes in the freight market, extreme volatility driven by economic or geopolitical shocks, and the role of external economic drivers, rather than focusing solely on methodological considerations.

The limitations and future research subsection has been rewritten to response to review’s concerns (p. 25, lines 788-812).

” Despite the strong forecasting performance of the proposed framework, several limitations should be acknowledged from an economic and market perspective. First, the dataset covers a relatively short time span, which may limit the model’s ability to capture long-term structural changes in the global freight market, such as shifts in trade patterns, regulatory interventions, or major economic cycles. As a result, the predictive results identified in this study may be less stable during periods of significant market restructuring or regime change.

Second, although the multi-stage hybrid structure is effective in extracting nonlinear patterns, it may face challenges under extreme market conditions, such as sudden freight rate surges driven by geopolitical events, supply chain disruptions, or abrupt demand shocks. In such environments, purely data-driven models may adjust less rapidly, potentially affecting short-term forecasting reliability.

In addition, the study adopts a univariate framework and evaluates only the Grey Wolf Optimizer (GWO) for weighting optimization, which limits the explicit inclusion of external economic drivers of freight market fluctuations, such as commodity prices, exchange rates, and financial market sentiment.

Future research may extend the proposed framework to a multivariate setting by incorporating economically meaningful variables. Recent studies show that commodity prices, exchange rates, and volatility indices significantly enhance BDI forecasting accuracy (Kim et al. [19]), while futures prices of aluminum, iron ore, cotton, thermal coal, and equity market indicators such as the NASDAQ Composite Index also exhibit strong explanatory power (Li et al. [22]). These factors can be integrated into an EMD-based hybrid framework using multivariate SVR or deep learning models. Moreover, alternative metaheuristic algorithms, such as Particle Swarm Optimization, may be explored to further improve robustness under highly volatile freight market conditions.”

We sincerely thank the reviewer again for these constructive comments, which have greatly improved the organization, and presentation of our paper.

 

Reviewer 2 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

The revised manuscript adequately addresses the issues I raised in the first submission. The presentation has improved, the methodology is now more clearly structured, and key modeling choices and evaluation criteria are clarified. I have no further substantive comments and recommend acceptance. Minor text-editing and copyediting revisions are still advised to ensure consistency and polish.

Author Response

Response to Reviewer 2

We sincerely appreciate the reviewer’s positive feedback and the time taken to evaluate our work. Below we address each point carefully and describe the corresponding revisions.

1. The revised manuscript adequately addresses the issues raised. I recommend acceptance, with minor text-editing and copyediting advised.

Response:

We sincerely thank the reviewer for the positive evaluation and recommendation. In response to the minor suggestions, we have conducted a comprehensive copyediting to improve consistency, clarity, and overall polish. This includes corrections to grammar, formatting, and notation throughout the manuscript.

We sincerely thank the reviewer again for these constructive comments, which have greatly improved the presentation of our paper.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

The article presents an interesting approach to forecasting the BDI index. However, the authors did not avoid mistakes, which are listed below:

1. The paper requires editing: the red color in the abstract should be changed, lines 40-45 are not edited in accordance with the journal's requirements, many lines in the literature review section are in red, and some abbreviations are not expanded (these are just a few of many comments).
2. Line 67 – abbreviation reintroduced
3. Figure 1 is illegible, Figure 7 and Table 6 should be re-edited.
4. The descriptive statistics presented in Table 2 are not described in any way.
5. All formulas require editing.
6. The axes in Figure 3 are missing a description.
7. Please clearly indicate the innovative nature of the presented tool.
8. The models are based on a very limited number of observations—particularly in the test set, which contains only a few cases. This raises a legitimate question about whether the LSTM and GRU models used are capable of producing reliable and stable results.
9. Figure 7 shows that none of the proposed models could cope with the sudden increase in values ​​in period 3 (?) or for 3 observations - the lack of an axis signature makes it impossible to clearly determine what the authors' intention was.

Author Response

Response to Reviewer 3

We sincerely thank the reviewer for the thoughtful and detailed comments that have significantly improved the quality and clarity of our paper. Below we address each point carefully and describe the corresponding revisions.

1. The paper requires editing: the red color in the abstract should be changed, lines 40-45 are not edited in accordance with the journal's requirements, many lines in the literature review section are in red, and some abbreviations are not expanded (these are just a few of many comments).

Response:

We apologize for these formatting issues. The manuscript has now been fully revised to comply with the journal’s requirements. Specifically, all red text has been removed, the abstract and literature review sections have been reformatted in accordance with the journal template, and all abbreviations are expanded at their first occurrence and used consistently throughout the manuscript.

 

2. Line 67 – abbreviation reintroduced

Response:

Thank you for noting this. The abbreviation at line 67 has been corrected to ensure consistent usage following its initial definition.

3. Figure 1 is illegible, Figure 7 and Table 6 should be re-edited.

Response:

All referenced figures and tables have been redrawn and reformatted to improve readability and resolution. Specifically, Figure 1 has been redrawn to enhance clarity, an x-axis label has been added to Figure 7, and the number of decimal places in Table 6 has been reduced to improve presentation.

 

4. The descriptive statistics presented in Table 2 are not described in any way.

Response:

 We agree and have added a dedicated paragraph in the manuscript explicitly describing and interpreting the descriptive statistics reported in Table 2, including distributional characteristics and their relevance to BDI forecasting.

The following paragraph has been added to the revised manuscript on page 16, lines 544-548.

“Table 2 summarizes the descriptive statistics of the monthly BDI data. The series has a mean of 1,743.264 and exhibits substantial variability, with a standard deviation of 851.541 and a wide range from 460.6 to 4,819.95. The positive skewness (1.244) and moderate kurtosis (2.380) indicate a right-skewed distribution with some extreme values. The sample consists of 68 monthly observations.”

 

5. All formulas require editing.

Response:

 All mathematical expressions have been carefully reviewed and reformatted using consistent notation and journal-compliant equation styling.

6. The axes in Figure 3 are missing a description.

Response:

Thank you for reviewer’s suggestion. Figure 3 (on page 17, lines 583-584) now includes explanatory captions to ensure clarity.

7. Please clearly indicate the innovative nature of the presented tool.

Response:

 Thank you for this valuable suggestion. We have revised the Conclusion sections to more clearly articulate the novelty and contributions of our research. Specifically, we will emphasize that our study introduces a hybrid EMD–SVR–GWO forecasting framework for the Baltic Dry Index forecasting problem and demonstrates how the GWO-based weighting mechanism enhances prediction accuracy compared to traditional and single-stage models (p. 24, lines 763-770).

 “In forecasting research, synergistic effects arise when multiple complementary methods are combined so that their strengths reinforce one another and improve overall predictive accuracy. In our model, the three-stage EMD-SVR-GWO framework creates such a synergistic effect because each method strengthens a different part of the forecasting process. EMD reduces noise and separates key patterns, SVR captures nonlinear relationships within each component, and GWO optimizes how these component forecasts are combined. Our model fills a methodological gap by offering a more robust way to capture the complex dynamics of the series.”

This clarification has helped readers better understand the paper’s scientific and practical contributions.

8. The models are based on a very limited number of observations—particularly in the test set, which contains only a few cases. This raises a legitimate question about whether the LSTM and GRU models used are capable of producing reliable and stable results.

Response:

 We acknowledge the reviewer’s concern regarding the limited sample size, particularly in the test set, and its implications for deep learning models. LSTM and GRU are included primarily as benchmark methods, and their results are interpreted cautiously given that deep learning models typically require larger datasets to achieve stable performance.

A paragraph on p. 24, lines 740–752, has been rewritten to clarify this point.

“According to Lewis’s MAPE-based classification, the proposed EMD-SVR-GWO model achieves a MAPE of 8.3455, corresponding to excellent forecast accuracy. In comparison, the ARIMA, SVR, and LSTM models yield MAPEs of 14.2829, 15.3686, and 16.3638, respectively, which fall within the good accuracy range, while the GRU and Grey Forecast models exhibit acceptable performance (with a MAPE of 24.0836 and 27.26, respectively). It should be noted that LSTM and GRU are included primarily as benchmark deep-learning methods, and their results are interpreted with caution due to the limited sample size, particularly in the test set. Deep neural networks typically require substantially larger datasets to fully exploit their representational capacity, and their comparatively weaker performance in this study likely reflects data constraints rather than inherent model deficiencies. Overall, the results consistently demonstrate the robustness and superior predictive accuracy of the proposed EMD-SVR-GWO framework for BDI forecasting under small-sample conditions.”

 

9. Figure 7 shows that none of the proposed models could cope with the sudden increase in values ​​in period 3 (?) or for 3 observations - the lack of an axis signature makes it impossible to clearly determine what the authors' intention was.

Response:

Thank you for reviewer’s comment. Figure 7 has been revised with clear axis labels. Additionally, more descriptions about the actual BDI have been added to the text to show BDI forecasting under extreme volatility (on page 22, lines 702-704).

“The actual BDI shows a sharp increase in the third period followed by a decline in the fourth period, after which it remains stable, reflecting short-term market volatility.”

We sincerely thank the reviewer again for these constructive comments, which have greatly improved the organization, and presentation of our paper.

 

 

Round 2

Reviewer 1 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

In every review, I write that Table 1 and Figure 3 are the same. Furthermore, the scale on the x-axis in Figure 3 is in Chinese. Furthermore, there is no presentation of the analyzed time series using descriptive statistics. This can be achieved in several ways. Thus, the authors make some corrections but do not fundamentally address the comments made.

Author Response

Response to Reviewer 1

We thank the reviewer for the continued careful reading of our manuscript and for reiterating these important points. We would like to clarify how each concern has been addressed in the revised version.

Reviewer’s comment: In every review, I write that Table 1 and Figure 3 are the same. Furthermore, the scale on the x-axis in Figure 3 is in Chinese. Furthermore, there is no presentation of the analyzed time series using descriptive statistics. This can be achieved in several ways. Thus, the authors make some corrections but do not fundamentally address the comments made.

Response:

1. Regarding the concern about redundancy between Table 1 and Figure 3

.We thank the reviewer for this comment. Table 1 and Figure 3 are intended to serve different purposes. Table 1 reports the numerical values of the monthly BDI series, while Figure 3 provides a visual representation of the same series to illustrate its overall trend and nonstationary behavior prior to modeling. To avoid redundancy, we have revised the caption of Table 1 (p. 15, line 533) and Figure 3 (p. 17, line 587) and discussion of Figure 3 to explicitly emphasize its exploratory and illustrative role rather than data presentation (p. 16, lines 539-543).

“Monthly Baltic Dry Index data from January 2019 to August 2024 are used in this study. Monthly values are obtained by averaging daily BDI observations from the Eastmoney database, yielding 68 observations. Table 1 reports the original monthly BDI data used in the empirical analysis to ensure transparency and reproducibility, while Figure 3 presents a graphical view of the series, illustrating its overall evolution and nonstationary behavior.”

 

2. the scale on the x-axis in Figure 3 is in Chinese.

Figure 3 (p.17, line 586) has been completely redrawn in the revised manuscript. All axis labels, including the x-axis, are now presented exclusively in English. We confirm that no Chinese characters remain in the figure.

3. there is no presentation of the analyzed time series using descriptive statistics.

Following the reviewer’s suggestion, a dedicated table of descriptive statistics has been added (Table 2), reporting the mean, median, standard deviation, variance, skewness, kurtosis, range, minimum, maximum, and number of observations. In addition, a corresponding explanatory paragraph (p. 16, lines 544-549) has been rewritten in Section 4.1 to discuss the distributional characteristics of the BDI series.

“Table 2 summarizes the descriptive statistics, highlighting the variability and right-skewed distribution of the data. The monthly BDI series has a mean of 1,743.264 and exhibits substantial variability, with a standard deviation of 851.541 and a wide range from 460.6 to 4,819.95. The positive skewness (1.244) and moderate kurtosis (2.380) further indicate a right-skewed distribution with some extreme values. The sample consists of 68 monthly observations.”

We hope that these revisions now clearly distinguish the roles of Table 1, Figure 3, and Table 2, and fully address the reviewer’s concerns.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

The authors have clarified all the questions/queries raised in the previous review.

Author Response

Response to Reviewer 3

We sincerely thank the reviewer for the careful evaluation of our revised manuscript and the positive feedback.

Reviewer’s comment: The authors have clarified all the questions/queries raised in the previous review.

Response:

We appreciate the reviewer’s confirmation and are grateful for the constructive comments that have helped improve the clarity and quality of the paper.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The introduction clarifies the importance of the Baltic Dry Index (BDI) and the four models adopted, but all four models are relatively outdated. Could some new comparative models be added?
2. The literature review section is well done, but it should more clearly compare the methods mentioned in existing literature with those tested in this study.
3. Some parts of the literature review seem fragmented and lack logical coherence.
4. The article introduces each prediction method in detail, but the rationale for combining EMD, SVR, and GWO is still insufficient. Why can these methods be combined into an effective prediction framework? Is there a synergistic effect between them, and how do they help improve prediction accuracy?
5. The article proposes future research directions, but more specific suggestions should be given. How to combine other variables to further improve BDI prediction accuracy?
6. The limitations of the model should be briefly discussed at the end of the paper.
7. There are some minor issues in format and English grammar.
8.  The comparison between predicted values and actual values is only presented in a table, which is not very intuitive. A line chart comparing predicted values and actual values is lacking.   9. The construction process of EMD-SVR-GWO currently has relatively much textual description. It is recommended to supplement a flow chart of model construction to enhance readability.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

I consider the objective of your research interesting; however, I have significant reservations about the way it has been carried out.

First, I would not classify this as a new method but rather as a sequence of applications of already well-established methods.

Second, a substantial portion of the exposition and the tables in the Data and Results section are unnecessary. For example, the detailed descriptions of several ARIMA models that are later discarded, as well as full software output screenshots, do not contribute to the paper. I would also note the redundant discussion of SARIMA at the beginning, which is not referred to later in the analysis.

Third, regarding the choice of method, one of the key statistical indicators—the coefficient of determination—has been omitted. The selected model shows an R² of 0.0181 on the test dataset, which indicates very weak predictive performance.

I will not elaborate on additional comments, since in my opinion the current paper cannot be sufficiently improved to meet the standards required for publication in a reputable journal such as Forecasting.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript investigates the predictive performance of four univariate approaches—Grey Forecast, ARIMA, Support Vector Regression (SVR), and the hybrid EMD-SVR-GWO model—using monthly Baltic Dry Index data from 2019 to 2024. The study aims to identify the most accurate model for short-term forecasting of the BDI, an important indicator for global shipping and trade. My comment are as follows:

[1] The mathematical expressions and symbols should be carefully revised to follow conventional notation standards. Several equations contain inconsistent formatting, including italicized parentheses and irregular symbol alignment. Ensuring uniform mathematical typesetting and standard use of parentheses, subscripts, and operators will improve readability and presentation quality.

[2] The manuscript should clarify the assumptions underlying Equation (1). Unlike stochastic time series models, the GM(1,1) framework does not require the data to be stationary or ergodic, and this distinction should be explicitly stated to avoid confusion with ARIMA-type approaches.

[3] (Line 209) The model-building steps for ARIMA (identification, estimation, and diagnostic checking) follow the classical Box–Jenkins approach, which is somewhat outdated. The authors may wish to acknowledge this and note that modern time series practice often relies on automated or information-criterion–based model selection procedures. Moreover, contemporary predictive modeling emphasizes out-of-sample predictive performance rather than solely the in-sample goodness of fit.

[4] (Line 210) The identification step based on visual inspection of ACF and PACF patterns reflects an outdated practice from the 1980’s Box–Jenkins approach. Modern time series analysis typically uses automated or information-criterion-based procedures for determining model order.

[5] The SVR section is not fully integrated with the time-series notation introduced earlier. The authors should clarify how the input–output pairs are constructed and how the SVR model produces forecasts that are consistent with those of the other methods.

[6] The methodological section reads as a patchwork of disconnected parts. The models are presented without a clear unifying framework, consistent notation, or logical progression. A thorough reorganization is recommended to improve coherence and methodological clarity.

[7] The data analysis section includes raw computer outputs and draft-style plots generated directly from software results. These should be replaced with properly formatted tables and publication-quality figures that ensure consistency in style, labeling, and interpretation throughout the manuscript. Furthermore, several methodological components are insufficiently discussed. Key modeling choices, parameter settings, and assumptions are presented without justification or interpretation. The authors should expand this section to explain the rationale behind each methodological step and clarify how these choices affect the forecasting results.

[8] The authors do not explain why ARIMA(1,0,0) was ultimately selected, despite ARIMA(0,1,1) having been previously identified. This inconsistency in the model selection process should be clarified, specifying the criteria or rationale that led to the choice of a different specification.

Final comments: The authors attempt to compare a short monthly time series using a mix of outdated statistical techniques and computationally intensive machine learning methods. Given the limited sample size, such complex models are prone to overfitting, which undermines the reliability of the reported results. A more parsimonious and statistically grounded approach would be advisable.

 

 

Comments on the Quality of English Language

The English language requires revision to correct several typographical, grammatical, and punctuation errors, as well as to improve overall fluency and consistency of terminology. A thorough proofreading or professional language edit is recommended before publication.

Reviewer 4 Report

Comments and Suggestions for Authors

An interesting article, but not entirely engagingly presented. A few suggestions:
1. The literature review refers to only 15 bibliographical items. So what kind of review is this? What is the research gap?
2. How does Table 1 differ from Figure 2? It is the same. I suggest presenting descriptive statistics in Table 1.
3. Clearly emphasize the added value. Better explain the novelty and significance of your findings.
4. Consider providing a deeper synthesis of your results, bringing some new theoretical findings with a higher level of generalization. There are no limitations identified in the analyses conducted.