Self-Weighted LSE and Residual-Based QMLE of ARMA-GARCH Models^†

Round 1

Reviewer 1 Report

The manuscript presents an investigation using the SWLSE of the ARMA model with GARCH noises. 
The authors present a study involving the statistical characteristics of the method. They use stock indexes as
case studies.

Some remarks:

1- The Introduction must discuss general aspects of the ARCH models, including real-world application and
relevant related works;
2- There are equations without numbering;
3- Page 1: Note the typo GRACH;
4- The results obtained by the proposed model do not present any comparison with other proposals. There are not
present any error metrics or statistical tests to evaluate the results.
5- the discussions are very poor, and there is no conclusion.

Although the authors present many equations, formulas, and proofs, the manuscript lacks practical aspects.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Review for the paper

Self-weighted LSE and Residual-based QMLE of ARMA–GARCH Models∗

The novelty of the project is justified and consists in Self-weighted LSE and Residual-based QMLE of ARMA–GARCH Model methodology. However, neither the approach itself nor the listed elements are well-established, and therefore not only a clear description of them is required, but also a justification, first of all, of the necessity and sufficiency of their application in just such a quantity, sequence of application, interconnection, complementarity.

In this paper, authors used some sources, containing both historical and fundamental works, as well as the latest scientific research on this topic. But the literature review can be structured. The papers discussed many points of this study. Please, discuss these papers:

An, J., Mikhaylov, A. (2020). Russian energy projects in South Africa. Journal of Energy in Southern Africa, 31(3). http://dx.doi.org/10.17159/2413-3051/2020/v31i3a7809

An, J., Mikhaylov, A., Jung, S.-U. (2021). A Linear Programming Approach for Robust Network Revenue Management in the Airline Industry. Journal of Air Transport Management, 91(3), 101979. https://doi.org/10.1016/j.jairtraman.2020.101979

At the same time, the above reflects the instrumental aspects, but the proposed tools are aimed at application, and therefore it is necessary to justify such an application to the selected object with the identification of its advantages in comparison with other methods used. In the absence of such information, the scientific novelty of the project seems unreasonable. Thus, the proposed tools are aimed at application, and therefore it is necessary to justify such an application to the selected object with the identification of its advantages in comparison with other methods used.

The comments presented above regarding novelty are valid for the analysis of the current state, therefore it seems that for a deep analysis of the current state, these comments should be eliminated. It is not clear how the effectiveness of the proposed method will be determined.

Authors need to add more details on the range of simulation considered in this work should be clearly outlined within the abstract and in Table 1 and Figure 1. The current statements are vague and too general to get an idea of the work that have been accomplished.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The paper "Self-weighted LSE and Residual-based QMLE of ARMA-GARCH Models" is interesting and addresses a relevant issue. Some issues should be enlightened:
- The final remarks and future works should be addressed;
- In practical applications, how the results can be useful?
- There are in the literature several hybrid systems that combine ARIMA with Machine Learning models to time series forecasting. The seminal work was proposed by Zhang [1]. How these hybrid systems can be benefited from the proposed method?   
- The english must be improved.

[1] Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159-175.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

accept