Effects of Interdependence and Contagion on Crude Oil and Precious Metals According to ρ_DCCA: A COVID-19 Case Study

Round 1

Reviewer 1 Report

Authors are going to determine the dependencies between Oil and metals prices in prepandemic and Covid-19 pandemic period and investigate the difference between their values. The topic is interesting and important. The article have extensive and detailed literature review. Anyway following version of the article require improvements in many aspects.

- The logreturns of analysed series usually have not long memory. The dependencies are short term. The obtained DFA is In most cases close to 0.5. It suggest only short-term correlation. The observed in the figure one long-term dependencies are consequence of nonstationarity of close quotations. Analyzed series have usually strong squared dependencies (multivariate ARCH effect)  I find, that applying DCCA is not good choice for such type of data.

- Authors made any initial analysis of the data (and descriptive statistics, tests etc)

- there is not argued convincingly why the dependence between oil and metals became stronger after pandemic beginning.

- there is not aplied any significance tests for DCCA and DCCA difference.

- I do not understood why Authors use the decadic logarithm except natural logarithm in the formula for daily logreturns? It does not make sense.

- Authors should not using links to Portuguese-language educational films in English-language journal.

Author Response

Reviewer 1

    Authors are going to determine the dependencies between Oil and metals prices in pre-pandemic and Covid-19 pandemic period and investigate the difference between their values. The topic is interesting and important. The article have extensive and detailed literature review. Anyway following version of the article require improvements in many aspects.
    
    This new version was improved.

    - The logreturns of analysed series usually have not long memory. The dependencies are short term. The obtained DFA is In most cases close to 0.5. It suggest only short-term correlation. The observed in the figure one long-term dependencies are consequence of nonstationarity of close quotations. 
        
    Look at the Table 3, with the auto-correlation exponent alpha_DFA (+-0.01), we can see three behaviors, that are:  persistence (with long-range correlation), alpha_DFA > 0.5 (WTI and Brent) All period; anti-persistence (with long-range correlation), alpha_DFA < 0.5 (WTI, Brent, Gold and Silver) period III;  and no memory case alpha_DFA =~ 0.5 (WTI and Brent) period I).

    -Analyzed series have usually strong squared dependencies (multivariate ARCH effect).  I find, that applying DCCA is not good choice for such type of data.
    
    We think that for these data, it is an excellent choice to apply the DFA method, as well as, the rho_DCCA cross-correlation coefficient (there are a large reference showing this, see for example ref. 6, 8, 9, 24).

    - Authors made any initial analysis of the data (and descriptive statistics, tests etc)
    See the Appendix A.

    - there is not argued convincingly why the dependence between oil and metals became stronger after pandemic beginning.

    See Figure 3 Delta\rho_DCCA for this case is > 0, this is our convincing result.
    
    - there is not aplied any significance tests for DCCA and DCCA difference.

    Our main objective was not to take into account the significance of the Delta\rho_DCCA results, but to show that COVID-19 had a clear influence on the contagion between crude oil and precious metals. However, based on Ref. 32, we can state that, for N=500 there is a significance level greater than 99% for contagion effect evidence.

    - I do not understood why Authors use the decadic logarithm except natural logarithm in the formula for daily logreturns? It does not make sense.

    Here, as we are talking about fluctuation analysis, whatever the base of the logarithm, the results for alpha_DFA and rho_DCCA will always give the same results.

    - Authors should not using links to Portuguese-language educational films in English-language journal.
    
    We added in the text (in Portuguese). 
    In this video, there is the possibility of putting the subtitles in English.

thanks for all comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

The Authors study the dynamics of the interdependence (pair-to-pair ) between WTI, Brent, Gold, and Silver. However, the relationship between WTI and Brent is not interesting; the differences are negligible, so the analysis could be reduced by focusing on just one of them (for instance, in the middle panel of Figure 2, we cannot detect any particular difference between the right and left figures). Probably it could be enriched introducing further commodities.

Minor comments:

Line 90: I would indicate the time series as x(t) and y(t).

Line 108: given that you have defined F^2_{DCCA,x:y}, I would define F_{DFA,x}

Line 119: specify that the video is in the Portuguese language

Line 146: you missed a "D"

English has to be seriously revised ("an case" in the title; "can defined" line 112; "tents to" line197; and so on)

Author Response

    The Authors study the dynamics of the interdependence (pair-to-pair ) between WTI, Brent, Gold, and Silver. However, the relationship between WTI and Brent is not interesting; the differences are negligible, so the analysis could be reduced by focusing on just one of them (for instance, in the middle panel of Figure 2, we cannot detect any particular difference between the right and left figures). Probably it could be enriched introducing further commodities.

    The main idea here was to present interdependence and contagion effect through the rho_DCCA coefficient in the presence of COVID-19 (theme of this special issue). Thus, if we take into account two Energy indexes, WTI and Brent, we can see that there is no contagion effect, because Delta\rho_DCCA =~0 (See Fig. 3), and there is maximum interdependence. However, if we cross these energy indexes with precious metals (Gold or Silver), we can see different behaviors, which is well evidenced by Delta\rho_DCCA in figure 3.

We think that, from the point of view of the main purpose of this paper and its special edition, new commodities would not change our conclusions, which is to study interdependence and the effect of contagion, by rho_DCCA coefficient.
    
    

    Minor comments:

    Line 90: I would indicate the time series as x(t) and y(t).
    We remade to $\{x_{i}\}$ e $\{y_{i}\}$, where "i" is the time moment,    1<= i <=Nmax

    Line 108: given that you have defined F^2_{DCCA,x:y}, I would define F_{DFA,x}

    Here we observe that F^2_{DCCA,x:y} is the generalization of F_{DFA,x} for two variables, then F_{DFA,x}=sqrt(F^2_{DCCA,x:x}).
    

    Line 119: specify that the video is in the Portuguese language
    We added in the text (in Portuguese). 
    Also, in this video there is the possibility of putting the subtitles in English language.

    Line 146: you missed a "D"

    Thanks for reading, it's now fixed.
    
    English has to be seriously revised ("an case" in the title; "can defined" line 112; "tents to" line197; and so on)
    
    In this new version we have improved the text.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

My emphasis has been given to the refinement of the article. The research  description is improved, and many flow are removed. I have only two remarks:

- there is lack of significance test for correlation. It means, that the conclusions about the strongness of correlation between are not perfectly legitimate

- Authors should going to better explanation of the reasons of the structure of dependence.

Author Response

My emphasis has been given to the refinement of the article. The research  description is improved, and many flow are removed. 
     Thanks

I have only two remarks:

- there is lack of significance test for correlation. It means, that the conclusions about the strongness of correlation between are not perfectly legitimate

   Figure 3 was remade, now with the null hypotheses at 99% of confidence level, based on REF [33].

- Authors should going to better explanation of the reasons of the structure of dependence.
 
  We have a new way of measuring interdependence and contagion effect (in times of crisis), based on recent papers by the complex systems group of PPGM UEFS.
  
  Thanks for all comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

This revised version is essentially the original version.

I cannot see any appreciable change.

The English language has been partially revised (I can see again "tents to").

In practice, the Authors did not make any effort to improve the paper.

Author Response

This revised version is essentially the original version. I cannot see any appreciable change.

     Certainly, this new version is based on the original version, mainly to measure the interdependence and the contagion effect (based on the rho_DCCA). But, as can be seen, a considerable change and improvements has been made, for example, with statistical test and a new figure 3 (with the significance test, for 99% CL, for Delta rho_DCCA).

The English language has been partially revised (I can see again "tents to").
 
     We change "tents to" for "tends to", as well as, other typographical errors have been corrected.

In practice, the Authors did not make any effort to improve the paper.

     We think yes, a great effort was made. Now, the paper fits within this special edition, as suggested by the editor.

     Thanks for all comments.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

I have no comment.

Author Response

Dear Reviewer,

     We produce a spell check for this final version.  We find some mistakes, that were fixed.

Thanks for all

Author Response File: Author Response.pdf