Statistical Analysis Dow Jones Stock Index—Cumulative Return Gap and Finite Difference Method
Round 1
Reviewer 1 Report
#1 The sample selection interval, why only select "the period of Apr. 1, 2010 to Jul. 8, 2016", is there any specific significance for such a sample interval selection?
#2 The author introduces different models. Which sources of these models are based on the author’s original research content? Which are the research content of other scholars? The author must have a systematic and clear explanation to present the content of the author’s research contributions.
#3 The author's mathematical expression, some of the estimated data of the parameters, should not be simply presented below the regression formula, so the regression formula is not a general way of presentation, and it does not conform to the rigorous mathematical presentation.
#4 All mathematical formula or regression formula parameters or variable symbols must be clearly defined and systematically displayed, so that the mathematical formula or regression formula can be clearly defined.
#5 The author only uses "A daily closing price index of Dow Jones Industry Index is used as time series samples." Subjectively, finite difference method is used to verify whether it can fully comply with "Cumulative return gap and finite difference method in stock return prediction". No Setting the title of any research scope is open to discussion. Unless the author can verify the sample of the main market and estimate the consistency of the model's application.
Author Response
Response to examiners report
Response:
Dear Examiner:
Thank you for your comments on the work. These comments are very important for the quality of this paper. I have revised the paper based on the comments and I have proofread my response to each comment in the following section, with explanations and changes made based on the comments.
Comment 1: #1 The sample selection interval, why only select "the period of Apr. 1, 2010 to Jul. 8, 2016", is there any specific significance for such a sample interval selection?
Response to comment 1: Thank you for this comment. This paper focuses on the presentation of the methodology, and we wanted to minimize the impact of COVID-19. Thus, the data were chosen more conservatively. An explanatory footnote (5) has been added to the original text on page 5.
Comment 2: #2 The author introduces different models. Which sources of these models are based on the author’s original research content? Which are the research content of other scholars? The author must have a systematic and clear explanation to present the content of the author’s research contributions.
Response to comment 2: Many thanks for your comment. Based on your comments, I have noted in the abstract that we exploit the valuable information contained in the residuals of the models in the context of cumulative return and construct a new cumulative return gap (CRG) model to overcome the weaknesses of the traditional cumulative abnormal returns (CAR) and buy-and-hold abnormal returns (BHAR) models.
Comment 3: #3 The author's mathematical expression, some of the estimated data of the parameters, should not be simply presented below the regression formula, so the regression formula is not a general way of presentation, and it does not conform to the rigorous mathematical presentation.
Response to comment 3: Thank you very much for your comment. I have used too many tables, which is why the presentation is structured as it is. This section has been revised in line with your comments. Non-essential expressions have been cut out.
Comment 4: #4 All mathematical formula or regression formula parameters or variable symbols must be clearly defined and systematically displayed, so that the mathematical formula or regression formula can be clearly defined.
Response to comment 4: Thank you for this comment. I have rewritten the Methodology part and modifying adding the footnote 6-8 to explain all parameters.
Comment 5: #5 The author only uses "A daily closing price index of Dow Jones Industry Index is used as time series samples." Subjectively, finite difference method is used to verify whether it can fully comply with "Cumulative return gap and finite difference method in stock return prediction". No Setting the title of any research scope is open to discussion. Unless the author can verify the sample of the main market and estimate the consistency of the model's application.
Response to comment 5: Many thanks for your comment. More rigorous proof is indeed needed here. I have added citations here: “A daily closing price index of the Dow Jones Industry Index is used as the time series samples (Ranco et al., 2015; Stekelenburg et al., 2015).”
Reference added:
Ranco, G., Aleksovski, D., Caldarelli, G., Grčar, M., Mozetič, I. (2015). The Effects of Twitter Sentiment on Stock Price Returns. PLoS ONE 10(9): e0138441. https://doi.org/10.1371/journal.pone.0138441
Stekelenburg, A., Georgakopoulos, G., Sotiropoulou, V. (2015). The relation between sustainability performance and stock market returns: An Empirical analysis of the Dow Jones Sustainability Index Europe. International Journal of Economics and Finance, 7 (7). ISSN 1916-971X
Author Response File: 
Author Response.docx
Reviewer 2 Report
The subject of the work (cumulative return gap in stock return prediction) is potentially interesting. In my opinion the description of problem (and a lot of results) are too long for paper in journal - I would suggest shortening the paper. In same places have to use references of research (e.g. line 50). Why Authors used this period (Apr. 1, 2010 to Jul. 8, 2016)? This selection requires justification because may affect the actual results. From the editorial point of view the paper is sloppy written (and formatted), and should be corrected e.g. no keywords, all formulas and graphs should be centered etc.
Author Response
Response to examiners report
Response:
Dear Examiner:
Thank you for your comments on the work. These comments are very important for the quality of this paper. I have revised the paper based on the comments and I have proofread my response to each comment in the following section, with explanations and changes made based on the comments.
Comment: The subject of the work (cumulative return gap in stock return prediction) is potentially interesting. In my opinion the description of problem (and a lot of results) are too long for paper in journal - I would suggest shortening the paper. In some places have to use references of research (e.g. line 50). Why Authors used this period (Apr. 1, 2010 to Jul. 8, 2016)? This selection requires justification because may affect the actual results. From the editorial point of view the paper is sloppy written (and formatted), and should be corrected e.g. no keywords, all formulas and graphs should be centered etc.
Response to comment: Thank you for your comments. This paper focuses on the presentation of the methodology, and we wanted to minimize the impact of COVID-19. Thus, the data were chosen more conservatively. An explanatory footnote (5) has been added to the original text on page 5. Your suggestions are valuable and we have had this paper revised by a professional editor and with a moderate reduction in word count. More rigorous proof is indeed needed here. I have added citations here: “A daily closing price index of the Dow Jones Industry Index is used as the time series samples (Ranco et al., 2015; Stekelenburg et al., 2015).”
Reference added:
Ranco, G., Aleksovski, D., Caldarelli, G., Grčar, M., Mozetič, I. (2015). The Effects of Twitter Sentiment on Stock Price Returns. PLoS ONE 10(9): e0138441. https://doi.org/10.1371/journal.pone.0138441
Stekelenburg, A., Georgakopoulos, G., Sotiropoulou, V. (2015). The relation between sustainability performance and stock market returns: An Empirical analysis of the Dow Jones Sustainability Index Europe. International Journal of Economics and Finance, 7 (7). ISSN 1916-971X
Author Response File: Author Response.docx
Reviewer 3 Report
The article is well written, informative and interesting. To improve the writing the authors need to write with shorter sentences and with active voice. The article needs a conclusion section. I read closely the text, tables, and figures. Amazing work. It's really a book, eminently publishable.
Please see the attachment with more detailed comments and suggestions.
Comments for author File: 
Comments.pdf
Author Response
Response to examiners report
Response:
Dear Examiner:
Thank you for your comments on the work. Much appreciated. These comments are very important for the quality of this paper. I have revised the paper based on the comments and I have proofread my response to each comment in the following section, with explanations and changes made based on the comments.
Comment 1: 1. I grade the paper 9 out of 10 on novelty, originality, and technical strength. The language performance needs improvement.
Response to comment 1: Thank you for your positive comments. Much appreciated. Your suggestions are valuable and we have had this paper revised by a professional editor and with a moderate reduction in word count.
Comment 2: I suggest revised title: “Statistical Analysis Dow Jones Stock Index 2010-2016: Cumulative Return Gap and Finite Difference Method”
Response to comment 2: Many thanks for your comment. The title now reads “Statistical Analysis Dow Jones Stock Index - Cumulative Return Gap and Finite Difference Method”
Comment 3: The article is well written, informative and interesting. To improve the writing the authors need to write with shorter sentences and with active voice. The article needs a conclusion section. I read closely the text, tables, and figures. Amazing work. It’s really a book, eminently publishable.
Response to comment 3: Thank you very much for your comment. I have used too many tables, which is why the presentation is structured as it is. After your suggestions we have had this paper revised by a professional editor.
Comment 4-75: Good.
Response to comment 4: Thank you for this comment. Much appreciated. Thank you for reading my paper so carefully and marking them individually, I admire your seriousness and dedication.
Comment 76: The article needs a conclusion section. I suggest: The empirical analysis results of ARDL-CRG-FD models have approved that improving the difference order of the probability variables can improve the determinate correlations of FD models; also when the difference order of the probability variables are fixed in second, third, or fourth order, improving the lag-order of the probability variable can improve the determinate correlations of FD models. When the FD model is fixed on the second-order finite difference regression model, after testing the lags of the probability variable d2qt(ab), the ARDLCRG-FD models and ARDL-CRG-GARCH-FD models have got three similar results: first, when the lag-order increases, the determinate coefficient for the regression model will increase; second, when the lag-order increases, the correlations between the real return index and its prediction values will increase; third, a higher lag-order prediction model can create a higher approximated result between the real return index and its prediction value. Thirdly, when compare the correlations between the real and predicted returns from the four kinds of models, it has approved: first, the CRG model can improve the prediction accuracy; second, the GARCH model has little impact on prediction values. Fourthly, when compare the hit ratios from the four different models, it has approved: first, the higher level of the lag-order has led to a higher hit ratio than the lower level of the lag-order when both of the return index and the prediction values are upward or downward together; second, the ARDL-CRG-FD model is better to improve the hit ratios than AR-FD models; third, the ARDL-CRG-GARCH-FD model on the hit ratios is similar to AR-GARCH-FD model; fourth, the AR-GARCH-FD models on the hit ratios is better than AR-FD models; fifth, the ARDL-CRG-GARCHFD models on the hit ratios is better than ARDL-CRG-FD models. Fifthly, when compare the RMSE test results from the four different models, it has approved: first, when the finite difference method is used, GARCH model cannot improve the prediction accuracy a lot; second, ARDL-CRGFD model can improve the prediction accuracy than AR-FD model; third, ARDL-CRG-GARCH-FD model has higher impact on the decrease of RMSE value than AR-GARCH-FD model; fourth, the CRG model can improve the prediction accuracy a lot.
Response to comment 76: Thank you for the excellent summary of the paper, which I have quoted in the original.
Comment 77: Reference Good.
Response to comment 77: Thank you for this comment. Much appreciated.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The reviewer does not have enough time to review the revisions of the author's context, please provide the revisions with a hightlight to clearly mark them, and also use lightlight to reply to the point by point of the question and reply to the revised content for the reviewer's review the revised manuscript more easily.
Author Response
Dear Examiner:
Thank you for your comments on the work. These comments are very important for the quality of this paper. I have revised the paper based on the comments and I have proofread my response to each comment in the attached pdf document, with explanations and changes made based on the comments.
Author Response File: Author Response.pdf
Reviewer 2 Report
Authors didn't answer the question, Covid appeared in 2020, and the period of research is 2010-2016, why not the period 2010-2019? Paper is incorrectly formatted
Author Response
Dear Examiner:
Thank you for your comments on the work. These comments are very important for the quality of this paper. I have revised the paper based on the comments and I have proofread my response to each comment in the attached pdf dcument, with explanations and changes made based on the comments.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
Well done all inquires than the previous version.
