Yule–Walker Equations Using a Gini Covariance Matrix for the High-Dimensional Heavy-Tailed PVAR Model

Round 1

Reviewer 1 Report

Comments are in the attached file.

Comments for author File: Comments.pdf

Author Response

Here we are first to thank the referee. The questions and concerns proposed by the referee improved our paper greatly.

We shall answer the referee' questions and concerns (in bold) one by one in

the following.

Author Response File: Author Response.pdf

Reviewer 2 Report

Paper presents the derivation of the Gini-Yule-Walker equation. Then, the authors use the method from Yang[16] to estimate Gini covariance and Gini mean difference (which appear in the Gini-Yule-Walker equation.) Thanks to the asymptotic normality of the estimators, the concentration results are obtained. Finally, based on the Gini-Yule-Walker equation, a novel method for estimating the transition matrix is proposed and shown to be competitive with existing methods.

I think that the overall presentation of the paper and the novelty make the paper worth publishing after a few adjustments. I listed below some comments that may help the paper improve.

Major Comments:

1) Gini-Yule-Walker equation is nicely derived. Authors may find it useful to include a discussion of the literature that uses the same or a similar equation. Then, comment on similarities and differences.

2) (Section 2.3) Why do the integrals over 0 to infinity? There is no restriction on either X or Y. I think the integrals should be over the whole real numbers, i.e. from minus infinity to plus infinity.

3) (End of line 75) It would be helpful to comment on orders. I think they stem from the estimator of Yang[16].

 

Minor Comments:

After line 76:
Two changes in the sentence "Next, we proof the convergence of the Gini covariance mtrix": 'prove' instead of 'proof' and 'matrix' instead of 'mtrix'. That is, "Next, we prove the convergence of the Gini covariance matrix"

After line 88:
"we proposed" should be changed to  "we propose".

Later in the same paragraph, "subproblemsthe" should be changed to "subproblems".

On line 139:  "we consider", the first letter should be capitalized: "We consider"

Overall in the whole paper, I think it is more appropriate to use "Dantzig selector" instead of just "Dantzig".

Again overall in the whole paper,  either "lasso" or "LASSO" should be used consistently. 

Author Response

Here we are first to thank the referee. The questions and concerns proposed by the referee improved our paper greatly.

We shall answer the referee' questions and concerns (in bold) one by one in

the following.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

My comments are attached in the file.

Comments for author File: Comments.pdf

Author Response

Here we are first to thank the referee. The questions and concerns proposed by the referee improved our paper greatly.

We shall answer the referee' questions and concerns (in bold) one by one in

the following.

Author Response File: Author Response.pdf