Predicting Random Walks and a Data-Splitting Prediction Region

Round 1

Reviewer 1 Report

I have carefully read the manuscript  stats-276983. The Authors compute nonparametric prediction intervals and regions for univariate and vector valued random walks with applications for renewal processes. The prediction of regions can be of interest for data distribution that does not have first moments or for high dimensional data where the number of predictors is larger than the sample size. The method is suitable to deal with data sets where the future data does not behave like the past data. Also, the use of a prediction region to data generated from a posterior distribution have been proved to give an estimated credibleregion for Bayesian Statistics. 

The proposed method to estimateregions is of interest in a random walk with an independent and identically distributed  drift.

Regarding the scientific aspect, the study is original, interesting and the methods employed seem to be robust and sound. From my previous comments, I think the manuscript warrants publication in Stats.

Author Response

Thanks for your work.

Reviewer 2 Report

The paper is well presented and it can be accepted after considering the following asked revisions:

1) The scientific merit and novelty of the article are not clear. The authors should explain clearly in the abstract what is the novelty of the proposed method and what is the added value in this article?
2) What is the motivation of the work? The problem considered does not have a sound motivation. The authors should clearly demonstrate the scientific interest of the objectives and results.

3) Authors are encouraged to discuss the possibility to use Machine learning models by discussing the following works:

- https://doi.org/10.12989/cac.2022.30.1.033

- https://doi.org/10.1016/j.enganabound.2022.08.001

4) Equation (8) should be checked.

5) Tables 2 and 3 should be more discussed.

6) I would encourage the authors to review the conclusion by introducing the main quantitative results presented in the paper.

The Quality of English is good.

Author Response

See the pdf file resprev2.pdf.

Author Response File: Author Response.pdf

Reviewer 3 Report

Please see attached. 

Comments for author File: Comments.pdf

Author Response

See the pdf file resprev3.pdf.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

I am satisfied with the current revision.