Discrete q-Exponential Limit Order Cancellation Time Distribution
Round 1
Reviewer 1 Report
The topic is interesting but need to revise before publication. Considered the following point:
(1) Introduction is not written in professional way. Take important key point and make comparative study with respect to present work and related published work.
(2) Need to cite important mathematical equation and important algorithm.
(3) Motivation is not clear as well as novelties also. It should be in introduction section as a separate heading.
(4) Add more remarks, note etc.
(5) Data sources should be properly cited. It should mention in different sub section also.
(6) Strengthen the introduction section by adding recent papers.
(7) Every figure should be briefly explained.
(8) Conclusion and future research scope should be extended.
(9) Comparative result should be added for showing the applicability of the work.
Revision needed.
Author Response
Response to Reviewer 1 Comments
Point 1: Introduction is not written in professional way. Take important key point and make comparative study with respect to present work and related published work.
Response 1: Thank you, we considerably improved the Introduction by extending the citation and rewriting the text.
Point 2: Need to cite important mathematical equation and important algorithm.
Response 2: We added eight new citations; for example, see section 2, where all essential mathematical equations are cited in the new version of the manuscript.
Point 3: Motivation is not clear as well as novelties also. It should be in introduction section as a separate heading.
Response 3: Thank you, we strengthened the motivation aspect of the text in the Abstract, Introduction, and even Conclusions.
Point 4: Add more remarks, note etc..
Response 4: I hope the new text has more remarks and notes.
Point 5: Data sources should be properly cited. It should mention in different sub section also.
Response 5: In the new version, the data source is cited more precisely in the text and subsection.
Point 6: Strengthen the introduction section by adding recent papers.
Response 6: We have added three very recent references in the Introduction.
Point 7: Every figure should be briefly explained.
Response 7: We extended figure explanations in the new version of the manuscript.
Point 8: Conclusion and future research scope should be extended.
Response 8: We have rewritten and extended the part of the Conclusions and Discussion.
Point 9: Comparative result should be added for showing the applicability of the work.
Response 9: The article is organized as a comparative analysis of order disbalance time series considered from the perspective of FLSM (already published) and a more specific approach based on the power-law distribution of limit order cancellation times. I hope the work's applicability is better revealed in the new version of the article text and Conclusions.
Reviewer 2 Report
The paper addresses an important research gap by investigating the statistical properties of limit order cancellation times in the context of order disbalance time series. The author asserts that the empirically established q-exponential nature of these cancellation times can aid in reconstructing properties of the order disbalance time series. The study's motivation to further explore auto-codifference in analyzing persistence in financial and social systems is commendable.
The author acknowledges the limitations of previous investigations that relied solely on the fractional Lévy stable motion (FLSM) concept to analyze order disbalance time series. By considering the peculiarities of empirical time series, such as the strict bounds observed in financial markets, the paper seeks to offer a more comprehensive understanding of the phenomena. The introduction of the discrete q-exponential distribution as a q-extension of the Geometric distribution is a logical choice, given the theoretical background in generalized Tsallis statistics.
The paper effectively distinguishes between limit order flow series and order disbalance series, emphasizing their distinct characteristics. The analysis reveals that limit order flow exhibits persistence and is unbounded, aligning with FLSM characteristics. On the other hand, order disbalance series, including order cancellations and executions, display bounded behavior and anti-persistence. This differentiation contributes to a clearer understanding of memory effects and the impact of cancellation times on order disbalance.
The proposed model, which combines fractional Lévy stable limit order flow with a q-exponential cancellation time distribution, offers a relatively simple yet potentially powerful framework for modeling order disbalance in financial markets. The author aptly highlights the broader applicability of such an approach to the modeling of opinion dynamics within social systems. This extension emphasizes the significance of social system modeling and the value of incorporating formal mathematical methods for accurate analysis.
Overall, the paper provides a valuable contribution to the field, presenting a comprehensive analysis of order disbalance time series and proposing a novel model that incorporates important empirical properties. The research findings open avenues for further investigations into the persistence and dynamics of financial and social systems. The paper is well-written, adequately references relevant literature, and makes convincing arguments.
In conclusion, the integration of Tsallis q-exponential distribution, FLSM, Hurst exponent, etc. provides interesting insights for studying limit order disbalances, and the proposed model has the potential to contribute to a better understanding of financial and social systems. This research significantly advances the current knowledge in the field and merits publication in a scientific journal.
Regarding the remarks:
1. I would add more references to the use of Tsallis statistics in economic science. You don't have to do an overview, but you could refer, for example, in the discussion to the prospects of using the same Tsallis triplet to study trade order imbalances. Here is one of possible references that you could include: Stosic, D., Stosic, D., & Stosic, T. (2019). Nonextensive triplets in stock market indices. Physica A: Statistical Mechanics and its Applications, 525, 192-198.
2. Little technical remark. Probably, in line 249, simple alpha has to be changed to mathematical symbol α
Author Response
Response to Reviewer 2 Comments
Thank you very much for carefully reading and evaluating our article.
Point 1: I would add more references to the use of Tsallis statistics in economic science. You don't have to do an overview, but you could refer, for example, in the discussion to the prospects of using the same Tsallis triplet to study trade order imbalances. Here is one of possible references that you could include: Stosic, D., Stosic, D., & Stosic, T. (2019). Nonextensive triplets in stock market indices. Physica A: Statistical Mechanics and its Applications, 525, 192-198.
Response 1: Thank you for the remark; we added two more references to Tsallis statistics, including your suggestion. The field of Tsallis statistics applications is vast and essential. Our findings in this research must be investigated from this perspective much more precisely. We will do it in further work.
Point 2: Little technical remark. Probably, in line 249, simple alpha has to be changed to mathematical symbol α
Response 2: We addressed this and other typos.
Reviewer 3 Report
The paper introduce a discrete version of Tsallis q-exponential distribution to model limit order cancellation times. It is known that order flow data in financial markets show signs of long-range memory observations though some researchers also try to explain them via nonlinear stochastic systems. Estimation of Hurst exponent as a measure of strength has also been challenging due to conflicting results from different estimators. The article briefly lists relevant references and contributions in the area but one wants to hear more about certain details including "contradictions revealed in the previous investigation ..." [20]. This is important to highlight the contributions of the current paper. There is some room to clarify certain statements and English content in the paper, especially in the introduction part. The abbreviations are mostly introduced properly but LOBSTR on page 1 (appearing first time there) has been explicitly stated in section 3. Other than that, the notation and equations seem standard and correct to me.
A few other comments for potential revision of the article are below:
1. Since the alternate approach has led to the intended discrete version in section 2, its motivation (e.g. as a generalization of the geometric distribution from Tsallis family) can be presented first. Then, the other (failed attempt) can be stated as a remark etc.
2. Estimation of parameters via MLE and cancellation time graphs in section 3 are suitable for this model. However, a statistical goodness-of-fit or an entropy measure of fit seem to support statistical analysis better than just the graphs or tables.
3. Random shuffling procedure for auto-dependence in the limit order volume data in section 4 looks interesting. One may want to hear more about the significance of variation in the Hurst exponent estimates.
4. Opinion dynamics in social systems has been referred a few times including in the abstract and conclusion. It may be useful to provide some details and references on such applications.
In short, this is a well-written and interesting empirical paper on statistical modeling of limit order cancellation times, and it can be improved by giving more attention to the clarity of the statements and a bit more formal statistical analysis.
I haven't noticed major grammar or language issues but I recommend that the author go over the revised version of the paper carefully (or get some assistance from a native English speaker) for improved clarity and for a more formal narrative of the article, especially in the introduction section (e.g. see the third paragraph). Moreover, it may be useful to get rid of excessive statements like "one must admit that", "one has to admit that", etc.
Author Response
Response to Reviewer 3 Comments
Thank you very much for your remarks. We have rewritten the whole text of the article addressing your and other suggestions. We cite LOBSTER data from the first mention.
Point 1: Since the alternate approach has led to the intended discrete version in section 2, its motivation (e.g. as a generalization of the geometric distribution from Tsallis family) can be presented first. Then, the other (failed attempt) can be stated as a remark etc.
Response 1: We followed your remark and improved Section 2.
Point 2: Estimation of parameters via MLE and cancellation time graphs in section 3 are suitable for this model. However, a statistical goodness-of-fit or an entropy measure of fit seem to support statistical analysis better than just the graphs or tables..
Response 2: We agree a statistical goodness-of-fit and entropy measure of fit would add value to this research. Nevertheless, we prefer to include this investigation in our further study, as the given time for the revision is too short.
Point 3: Random shuffling procedure for auto-dependence in the limit order volume data in section 4 looks interesting. One may want to hear more about the significance of variation in the Hurst exponent estimates.
Response 3: We used random reshuffling in our previous paper as the main instrument to validate autocorrelation. In this paper, we rely more on auto-codifference. From our point of view, these methods complement each other.
Point 4: Opinion dynamics in social systems has been referred a few times including in the abstract and conclusion. It may be useful to provide some details and references on such applications.
Response 4: Our primary scientific interest is the opinion dynamics in social systems. Some additional references to our previous work are included in the new version of the Introduction. The definition of order disbalance, as we use in this research, can be viewed as a measure of opinion in the financial market. Thus, limit order cancelation time may be considered as an opinion lifetime. We expect to develop this point of view in our further research.
Reviewer 4 Report
Report on the paper
Discrete q-exponential limit order cancellation time distribution
by Vygintas Gontis
The author's aim is to continue his previous 'analysis of the order flow LOBSTR data to demonstrate that ... simple enough modeling of empirical time series is possible'.
The author uses an application of Tsallis statistics to an established collection of stylized facts.
The main gain of the paper is a relatively simple model of order disbalance in the financial markets, obtaining an example of the more general approach to the modeling of opinion dynamics.
I recommend the work be published.
Author Response
Response to Reviewer 4 Comments
Thank you for your positive paper evaluation.
Round 2
Reviewer 1 Report
The author give the revision very successfully. I strongly recommended it for publication.
Extensive editing of English language required
