Modeling and Forecasting Time-Series Data with Multiple Seasonal Periods Using Periodograms
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article is well written, however, it requires some modifications:
• The citations in the text should be completely revised and placed in APA format. When referring to the authors' work, expressions such as "She" or "He" should be eliminated and a more informal style should be used, such as "the author says that [...]".
• It is necessary to separate the introduction from the analysis of the reference scientific literature. The introduction must contain the research question, the originality of the scientific contribution produced, the gap with the existing literature. In the analysis of the literature, however, which must constitute a separate section following the introduction, the reference scientific articles must be analyzed, in a critical and research-oriented way.
• The articles cited must be recent. That is, it is necessary to cite and discuss the articles produced between 2020 and 2025.
• At the end of the introduction, it is necessary to summarize, even with a single sentence, the contents of the subsequent sections.
• Having used a public dataset present on Kaggle, it would also be a good idea to report any other articles that have used the same dataset and check whether they have produced results useful for the analysis.
• In paragraphs 2.2.1 and the following 2.2.2, it is not necessary to report the full results of the analysis by Alysha M. De Livera et al. (2011). On the contrary, it would be necessary to highlight the specific contributions that this mathematical treatment brings to the analysis proposed by the author. That is, the citation must be finalized to the proposed analysis.
• The reference to Table 1 must be inserted in the text before the presentation of the same table.
• In the analysis of seasonalities, only short-term results are identified. That is, seasonalities detected at a daily or sub-daily level are identified. In this sense, it is necessary to consider that this hypothesis is not plausible. In fact, there is certainly also a longer seasonal dimension in the data that concerns the succession of the seasons. Electricity use should have peaks for example in summer due to home refrigeration systems, and also during the winter months due to the reduction in hours of outdoor light. Furthermore, there should also be an increasing trend in the period considered. In fact, energy consumption tends to be increasing because economies tend to become energy-intensive both as a result of economic growth and following the spread of new technologies.
• Since the article is full of acronyms, it is necessary to introduce a table of acronyms.
• Figure 8 highlights the ability to predict trends of the proposed models. However, in the same image it is evident that the models do not have the ability to predict peaks in distribution. It should be emphasized that a correct representation should also associate tools for predicting peaks in energy consumption.
Through the application of the proposed changes it is possible to make the article more interesting for publication purposes.
Author Response
Dear Reviewer:
Your thorough review comments and suggestions greatly improved the manuscript, so thank you very much. We have taken the time to consider your feedback and have made the appropriate revisions to our manuscript based on your comments. Really, we appreciate your knowledge regarding the subject matter. We used the color yellow to highlight the changes in the manuscript.
Once again, we are deeply grateful.
Reviewer’s Comments and Authors’ Responses:
Reviewer’s Comment 1: The citations in the text should be completely revised and placed in APA format. When referring to the authors' work, expressions such as "She" or "He" should be eliminated and a more informal style should be used, such as "the author says that [...]".
Authors’ Response 1: Thank you for pointing the issue out. We revised citations in the text and updated the references in APA format, highlighting them in turquoise/ bright green color. Furthermore, we changed the word” she” to “the author says that” on page 15 and highlighted it in yellow.
Reviewer’s Comment 2: It is necessary to separate the introduction from the analysis of the reference scientific literature. The introduction must contain the research question, the originality of the scientific contribution produced, the gap with the existing literature. In the analysis of the literature, however, which must constitute a separate section following the introduction, the reference scientific articles must be analyzed, in a critical and research-oriented way.
Authors’ Response 2: Thank you for your constructive comments that modify our article’s introduction and literature part. We separated the introduction and literature review part on Page 2 and highlighted it in yellow. In the same page of the manuscript, we highlighted the research objectives, originality, and the gap within the existing literature in yellow.
Reviewer’s Comment 3: The articles cited must be recent. That is, it is necessary to cite and discuss the articles produced between 2020 and 2025.
Authors’ Response 3: We appreciate your suggestion. We included the references from 2020 to 2025 on pages 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, and 18. It is highlighted by bright green color.
Reviewer’s Comment 4: At the end of the introduction, it is necessary to summarize, even with a single sentence, the contents of the subsequent sections.
Authors’ Response 4: Thank you for your valuable insight. We summarize and put the necessary recommendation in the end of introduction part (Page 2), and highlighted by yellow color.
Reviewer’s Comment 5: Having used a public dataset present on Kaggle, it would also be a good idea to report any other articles that have used the same dataset and check whether they have produced results useful for the analysis.
Authors’ Response 5: Thank you for your suggestion to improve the quality of references. We have primarily reviewed the reference of Velasquez et.al. (2022). The paper titled "Analysis of time series models for Brazilian electricity demand forecasting" was published in Energy, 247, 123483. And we included the literature review on page 4, highlighted by the yellow color.
Reviewer’s Comment 6: In paragraphs 2.2.1 and the following 2.2.2, it is not necessary to report the full results of the analysis by Alysha M. De Livera et al. (2011). On the contrary, it would be necessary to highlight the specific contributions that this mathematical treatment brings to the analysis proposed by the author. That is, the citation must be finalized to the proposed analysis.
Authors’ Response 6: De Livera et al. (2011) developed the BATS and TBATS models to model and forecast time series analysis using multiple seasonal periods. They used the Seasonal Decomposition (STL or Classical Decomposition) technique to separate the time series into trend, seasonal, and residual components. Then they identify the seasonality as daily, weekly, monthly, and yearly based on their cyclic periods. On the other hand, we used the spectral density technique, which relied on the periodogram method as the main seasonality selection method, by putting together with mathematical formula. We included this suggestion on manuscript page 6 and 7, and highlighted by yellow color.
Reviewer’s Comment 7: The reference to Table 1 must be inserted in the text before the presentation of the same table.
Authors’ Response 7: Thank you for your comment. We inserted the reference for Table 1 on page 8.
Reviewer’s Comment 8: In the analysis of seasonalities, only short-term results are identified. That is, seasonalities detected at a daily or sub-daily level are identified. In this sense, it is necessary to consider that this hypothesis is not plausible. In fact, there is certainly also a longer seasonal dimension in the data that concerns the succession of the seasons. Electricity use should have peaks for example in summer due to home refrigeration systems, and also during the winter months due to the reduction in hours of outdoor light. Furthermore, there should also be an increasing trend in the period considered. In fact, energy consumption tends to be increasing because economies tend to become energy-intensive both as a result of economic growth and following the spread of new technologies.
Authors’ Response 8: Thank you for this valuable suggestion. And we included it on pages 4 and 13, highlighted by the gray and yellow color respectively.
Reviewer’s Comment 9: Since the article is full of acronyms, it is necessary to introduce a table of acronyms.
Authors’ Response 9: Thank you for valuable feedback. We introduced the Table of acronyms on page 21, highlighted by the yellow color.
Reviewer’s Comment 10: Figure 8 highlights the ability to predict trends of the proposed models. However, in the same image it is evident that the models do not have the ability to predict peaks in distribution. It should be emphasized that a correct representation should also associate tools for predicting peaks in energy consumption.
Authors’ Response 10: Thank you for the valuable recommendation. The manuscript already includes Figures 2 and 4 on pages 11 and 12. We use dominant seasonality as a measurement to identify the peaks in each seasonality's distribution. In addition to that, we included the literature review on page 4, highlighted by the gray color.
Thank you for your time and understanding. We learned a lot from your constructive comments and suggestions.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe attached file contains all the comments.
Comments for author File: Comments.pdf
Author Response
Dear Reviewer:
Your thorough review comments and suggestions greatly improved the manuscript, so thank you very much. We have taken the time to consider your feedback and have made the appropriate revisions to our manuscript based on your comments. We used color to highlight the changes in the manuscript.
Once again, we are deeply grateful.
Reviewer’s Comments and Authors’ Responses:
Reviewer Comment 1: The researcher addressed an important topic and used appropriate statistical tools, especially since prediction methods are developing day after day and computers are being applied, in addition to advanced statistical programs such as Minitab, Stat graphics and SPSS, which enable us to deal with research data and process all transformations and extreme values in it, which affect statistical analysis and may give false results.
Authors Response 1: Thank you for your appreciation.
Reviewer Comment 2: In Table 1, the researcher used the variance measure, and it would have been better to use the standard deviation instead of the variance, because the standard deviation is measured in the original units of the data, unlike the variance, which is measured in square units. Here, it is easy to take the square root of the variance value in Table 2.
Authors Response 2: Thank you for pointing the issue out. We agree with this comment. Therefore, we have made the necessary modifications in Table 1 to address this point on pages 8 and 9, and highlighted with light pink color.
Reviewer Comment 3: In the second figure, the researcher used Histogram to show the difference between the original data and the transformed data. Here, I suggest that the researcher use the following transformation, and the graphical figures illustrate this.
It is noted from the two figures that the transformation method is using the Box-Cox method.
Authors Response 3: Thank you for pointing the issue out. We appreciate your suggestion. Similarly, we followed the same steps as you showed in the figures. In our Figure 2, we compared the normal distribution of the original and transformed data. Before that, we calculated the “Optimal Box-Cox Lambda” value using R software, as you suggested in the two figures. Then, we calculated the best lambda value, which is 0.68. This value is the minimum estimated value in the 95% CI, like the value you calculated in the comment 3 figure: 0.76. In our second figure of Figure 2, we used this (0.68) lambda value to plot the histogram to check its normality and compared it with the first plot for the original data. Then, we used the Box-Cox transformed data for further analysis since it showed a better normal distribution than the original data. As evidence, we put the list of R codes below.
# Checking the lambda value of the original data
> lambda_value <- BoxCox.lambda(BrazilData) # Its lambda value is 0.68, so the BoxCox transformation be needed.
> # BoxCox transformation uses to stabilizing variance, Achieving normality, improving forecasting, Handling outliers, and Adjusting for seasonality and trend effects.
> lambda_value
[1] 0.6752169
> # library(forecast)
> # Calculating the optimal lambda
> lambda_best <- BoxCox.lambda(BrazilData)
> print(paste("Optimal Box-Cox Lambda:", lambda_best ))
[1] "Optimal Box-Cox Lambda: 0.675216921372371"
> # Box-Cox transformation
> Box_TraLnsformed <- BoxCox(BrazilData, lambda = lambda_best)
We included your suggestion on manuscript page 10, highlighted by light pink color, in line with our software that we used.
Reviewer Comment 4: I suggest that the researcher use the following test to detect the presence of seasonality in the data, called the Kruskal-Wallis test, and compare the test values with the table chi-square values. If the KW value is greater than the table chi-square value, this indicates the presence of seasonality in the data.
Authors Response 4: Your suggestion is really appreciated. Unfortunately, the Kruskal-Wallis test was not used. Like one-way ANOVA, the Kruskal-Wallis test is a non-parametric statistical test used to identify variations among the medians of three or more independent groups. In their 2021 publication, Hyndman, R. J., and Athanasopoulos argue that time-series-specific methods should be employed instead of tests such as Kruskal-Wallis. As our understanding, the Kruskal-Wallis test isn't the best option for studying seasonality since it doesn't take temporal ordering of data into account, and seasonality is something that happens over time. Additionally, time-series data may not be independent due to the correlation between observations over time, and the test assumes that the groups are independent.
Kwiatkowski, Phillips, Schmidt, and Shin (KPSS), and Hylleberg-Engle-Granger-Yoo (HEGY) are two of the best seasonality tests that included in our study.
Thank you for your time and understanding. We learned a lot from your comments and suggestions.
Author Response File: Author Response.pdf
