Hierarchical Time Series Forecasting of Fire Spots in Brazil: A Comprehensive Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is attractive due to its application. A hierarchical approach to fire spot forecasting is auspicious. The methods are well-known and very popular in research. The paper is clear and well-constructed.

I found some issues that should be explained:

1. It would enhance the paper if the authors indicated its novelty in the introduction.

2. In the end, it is said that: "In summary, this study contributes valuable insights into applying forecasting reconciliation in fire spot forecasts." That is true, but other methods were also used to forecast fire spots in Brazil. Discussing the findings presented in the literature would provide a better understanding of the results described in this paper and increase the research standards.

2. Concerning the methodology:

- ARIMA model is selected using AIC. This criterion typically indicates a broader model. Alternatively, BIC indicated a more parsimonious model. These two criteria should be presented. An explanation is needed as to why AIC was selected.

- RMSE is the main criterion of forecast comparison. Is it enough? It has some advantages and disadvantages as well. It is recommended that more indicators be provided to compare the forecasts—at least mean absolute error.

 

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses hierarchical time series forecasting of fire spots in Brazil. I recognize that the topic is interesting, but the motivation of the research objective and the literature review are insufficient, and the methodology has serious limitations. For example, no exogenous variables are exploited, and this questions the accuracy of the predictive models. A literature review could be useful in this sense. Also, data are counts, therefore INGARCH models are the most appropriate method (Ferland et al., 2006), but they are ignored.

Other comments:
- in the abstract, the mention to the metrics employed is trivial. I suggest to remove it;
- descriptive statistics of the data are missing;
- the split into train and test sets is arbitrary: for time series, it would be more rigorous to use rolling window cross-validation.

Ferland, R., Latour, A. and Oraichi, D. (2006) Integer-valued GARCH process. Journal of Time Series Analysis 27(6), 923-942. DOI: 10.1111/j.1467-9892.2006.00496.x

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

 

This paper presents a review of different statistical forecasting

methods and a comparison of their skills at foracasting fire spots in

Brasil from 2011 to 2022, when used with different hierarchical

approaches. The methods applied are the well known ARIMA method,

 

the Exponential Time Smoothing (ETS) and the so called prophet

model, that incorporates an estimation of trends, sesonal patterns,

and working days characteristics to the forecast. These methods

qare applied on the time series previously smoothed. Two measures 

are used to assess the forecasting performance.

The Introduction seems clear and adequate, however the methodology leaves unclear many important aspects, and paradoxically, some sentences in the Introduction are literally reproduced in the Methodology section. The scheme in Figure 2 illustrates only one part of the forecast procedure: a complete flow chart of the procedure followed would be more appropriated. The figure captions that illustrate the data and results have also shortcomings: missing geographical coordinates, lines that are crucial to understand the plots not described. Results are not clearly summarized and the importance of the differences among the skill attained with the different forecasts are not clearly discussed. Then although the paper provides an interesting insight in the field of hierarchical time series forecasting, some improvements in its presentation on the aspects detrailed below are recommended before publication.

1- Figure 1 in the Introduction lacks geographical coordinates. It also would be better if Brazil was presented in an extended map of the region, with the Atlantic ocean position marked.

2- Line 41 – Could the expression ‘In the bottom up method’ mean ‘In the bottom down method’

3- The sentence ‘The bottom-up approach … to obtain forecasts for the levels above’ in lines 39-41 is reproduced in lines 110-111.

4- The sentence ‘In the bottom-up method, the total series is forecast,….disaggregated for the lower levels’ of line 41 is reproduced in lines 122-123.

5- In the sentence ‘In the middle-out approach, a middle level is chosen, ... while the top-down approach is applied to the levels below’ of lines 42-44 is reproduced in lines 150-153-

6- For a comprehension at a glance, a flow chart of the forecast procedure followed, with the data transformation step, the forecast procedure followed, the data transformation reversion (if any, this is one of the unclear aspects) and the skill quantification, would be very convenient.

7- As the advantages of using the bottom up approach are stated at the beginning of this method description (lines 112-113), it would be convenint to follow the same scheme with the description of the other approaches.

8- Expression 5 after line 213. This is one of my main objections to the present drafting. Effectively the ARIMA model CAN be described by expression (5) but it IS NOT usually described by expression (5). It is the state vector which uses to appear in the expression instead of the fluxes (derivatives in time) which appear in (5). Effectively, the expression (6) can be derived from the customary ARIMA expression, but the differenciation has to be justified, because some information is lost. It has to be stated also clearly how the original state variable is recovered.

8- Are the skills computed with respect to the original variable or with respect to the transformed variable?

9- The red line in the figures 8 and 9 is not described in the figure caption.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors addressed very carefully the issues I raised. I think that the manuscript is suited for publication after the following minor changes:
- Line 220: a typo: 'demoted' should be 'denoted'.
- Line 257: formula and citation for the AICc should be provided. For example, consider citing Sugiura (1978).
- Line 315: if I am not going wrong, it seems that y[t] with hat, which represents the predicted value at time t, is undefined.
- Not mandatory: what about inserting the literature review into a separate section, after the introduction?

Sugiura, N. (1978), "Further analysis of the data by Akaike's information criterion and the  finite corrections", Communications in Statistics - Theory and Methods, 7: 13–26, doi:10.1080/03610927808827599

Author Response

Please see the attached document.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

 The authors have corrected the text according to the reviewers comments. As a consequence, we think the manuscript is now ready to be published in the Stats journal.

Minor comment : The mentions to the acronym Mint through the text must be unified, either MinT or MINT.

Author Response

Comment 1: The authors have corrected the text according to the reviewers comments. As a consequence, we think the manuscript is now ready to be published in the Stats journal.

Minor comment : The mentions to the acronym Mint through the text must be unified, either MinT or MINT.

Response 1: We thank the reviewer for revising our manuscript again. The required change was made.