A Unified Grey Riccati Model
Round 1
Reviewer 1 Report
The Authors in order to reduce the computational complexity of the time response function, this study attempts to transform the Riccati equation into a Bernoulli equation with the help of a known particular solution. Then a unified time response function of GRM is obtained by the proposed methodology. Simulation results demonstrate that the proposed unified grey Riccati model performs the same as the grey generalized Verhulst model (a kind of grey Riccati model) and is better than the traditional grey Verhulst model. The fact also reveals that the newly developed grey Riccati model is reasonable and effective. Please add some information about future work.
Author Response
In the revised paper, the authors had added the following statements into the second paragraph of Conclusions Section:
“Some future works of this study may be concerned in the near future. The first issue is how to further enhance the modeling and forecasting performances of the unified grey Riccati model. The issue may be solved by optimize the undetermined coefficient C as the N_Verhulst model does or other optimization methods. The second one is applied to the real-time time series forecasting problem to demonstrate the practical application ability of the proposed grey model.”
to demonstrate the future works of this study.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The article touches on an important and relevant topic.
In general, the authors provided a good overview of the subject area under consideration.
The authors carefully presented all the mathematical calculations.
However, one should look more closely: all formulas require explanations regarding the variables used.
For example, what is the k in the second paragraph on the second page (?(1)(?))?
I think it is necessary to strictly justify the use of such a large number of decimal places for some numbers (from 5 to 8).
I suggest adding a Discussion section.
Author Response
Comment 1:
All formulas require explanations regarding the variables used. For example, what is the k in the second paragraph on the second page (z(1)(?))?
Response:
In the revised paper, the authors had rewritten the statement as
“… The background value at the time instant k, i.e. z(1)(?), [12,13], …”
to explain the variable k.
Comment 2:
I think it is necessary to strictly justify the use of such a large number of decimal places for some numbers (from 5 to 8).
Response:
In order to compare the proposed grey model with the traditional Verhulst model and N_Verhulst model in Section 4, the representation of the simulated data given in Tables 1 and 2, the values of the model parameters and the coefficients in the equations are the same as those given in [7]. Therefore, the decimal places of the simulated data, model parameters and coefficients may be different due to different precision.
Comment 3:
I suggest adding a Discussion section.
Response:
In the revised paper, the authors had added a new subsection, termed “Discussions” in Section 4 to briefly discuss the results obtained by this study.
Author Response File: Author Response.pdf
