Dear authors,

Four reviewers have now provided comments on your revised manuscript. From their comments it appears that you made significant improvement in your manuscript and that your paper provides a good contribution to scientific progress. However, all of them pointed out several parts of the paper that still MUST be revised before the paper can be considered for publication. In particular, the reviewers indicated that part of the discussion is not convincing (for them and probably not for the reader). You will see these comments in detail in their reviews. However, I want to underline several major issues here.
- I am concerned with the comment of referee#2 who wrote that section 4.2 do not support the last sentence of the abstract.
- The reviewers also underlined that robustness of the results is not properly evaluated. Your analysis is missing support of numerical values. For example, you cannot only write that data series are visually correlated, you must prove it. A more quantitative analysis of your results is requested. The reviewers made suggestion to improve this, for example with Monte Carlo or by computing correlations.
- I will not repeat comment 2 from referee#3. However, it is extremely important that this comment is fully addressed and that the manuscript is revised accordingly. Maybe a sensitivity test on the choice of the frequency bands could help here.
- Referees#4 provided a list of questions/comments. Some are essential but easy to answer, for example providing missing references. I strongly encourage you to answer carefully all these comments.
- Section 4.2 seems to be a weak point of your paper. I invite you to consider either (1) provide solid and robust elements that support the analysis (see some suggestions from the reviewers) or, if this proved to be too difficult, (2) to reduce this section and to provide more cautious conclusions on the millennium case.

At last I must urge you to address and reply ALL the referee’s comments and to amend your manuscript accordingly. Your revised paper will again be sent to the referees before any final decision be taken.

Thank you for the detailed answers to the comments, questions and suggestions of the referees. There are still some remaining issues that I listed here.
1. You did not answer to the comment/request of the referee #3 who asked ‘to explicitly write that it is a linear point of view, especially in the abstract and conclusion.’ Please do so.
2. I invite your to include the values of the MTM and redfit parameters directly in the paper (caption of the figure for example) instead of in an appendix.
3. In the response to referee#3 (Item 7a) you answered that you linearly interpolated the data. However the word ‘linearly’ has been forgotten in the main revised text (pag 5, line 25).
4. Please include figure R1 into your manuscript.

Thank you for preparing your revised manuscript following the referee recommendations.