Analytical Formulas for Conditional Mixed Moments of Generalized Stochastic Correlation Process

Round 1

Reviewer 1 Report

This paper deals with a class of diffusion processes, which have constant parameters as well as time-dependent parameters with restricted to a finite. The conditional moments based on Jacobi process with time-dependent parameters have been proposed. For applications, some estimation of parameters methods based on the moments are discussed.

 

All in all, I think this paper is interesting. The results is new and the calculation is correct. My concerns are:

1. Experimental validation: I suggest the author should share the software code using github or your home page.
2. Method of moments estimator: How to obtain the estimators using the system of equations fn(θ) = 0? The authors should provide some algorithms in details.
3. Page 16: are these Method of moment estimators consistent? All the estimators have asymptotic distribution in large sample?

Author Response

Thank you for your time that you spend on checking all the calculation. Please see the responses to your comments in the file attached.

Author Response File: Author Response.pdf

Reviewer 2 Report

The Jacobi stochastic process ia an explictly solvable diffusion process widely used in many application fields, including for example mathematical finance. For this process analytical formulae for conditional mixed moments are deduced using the Feynman Kac formula. The formulae deduced my be used in the solution of identification and inverse problems. That is they may be used to determine the parameters of the Jacobi process starting from observations. 

The formulae can be deduced in many different ways combining the analytical tools of the diffusion processes theory. The paper is not very innovative however a finished and useful piece of work is presented.

English style is not always satisfactory. The paper will benefit from being carefully edited before being published.

I suggest to accept this paper for publication.

Author Response

Thank you for your time in reviewing this paper. We have carefully checked all the English style throughout the paper.

Reviewer 3 Report

This work is aimed at studying conditional moments based on the Jacobi process with time-dependent parameters. The research results are extended to generalized stochastic correlation processes. All statistical properties, such as variance, covariance, and correlation, are presented analytically. It should also be noted. What is an illustration of the application of the proposed formulas. The article is written in a very good style and meets the requirements of the journal. Therefore, it can be recommended for publication.

Author Response

Thank you for your time in reviewing this paper. We mention about the applications of the proposed formulas in Sections 3.3 and 5 that are “Statistical Properties” and “Method of Moments Estimator” on pages 13 and 16 of the revised manuscript.

Reviewer 4 Report

I have some observations which are given below:

(i) Why authors are highlighted by red colour inside the manuscript? Is it revised version?

(ii) Abstract should be concise.

(iii) Introduction is not enough for publishing.

(iv) What is the research contribution?

(v) Check all the mathematics carefully.

(vi) What is the practical implication.

(vii) Rewrite the conclusion carefully. 

Based on the above mention comments minor revision is required.   

Author Response

Thank you for your comments and suggestions. The responses to your comments are in the file attached.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All my concerns have been answered. It is fine. 

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.