On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading
, Ilya Shirokov 2,†, Yuri Dernov 2,†and Luz Adriana Guzman Trujillo 3,†
Round 1
Reviewer 1 Report
See the attached file.
Comments for author File: 
Comments.pdf
The written English should be checked.
Author Response
I have submitted my reply to Reviewer #1.Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
I found the topic of this paper interesting. Could the authors please address the following comments and questions?
1. Section 3 is called "Advanced Statistical Description of the Stock Market Data," but it deals mostly with statistical assumptions, rather than an "Advanced Statistical Description".
2. The financial meaning of the optimization in Section 4 is unclear. In finance, optimization is typically based on a combination of maximizing expected profit and minimizing risk. How is the optimization in Section 4 consistent with the goal of maximizing expected profit and minimizing risk?
3. Throughout the paper, the authors talk about the stock market but then implement the results for BTC/USDT futures, which refer to a cryptocurrency pair and not a stock.
4. For the implementation, the authors should check if the log-normal assumptions made in Section 3 are not rejected using a statistical test, for example, the Jarque-Bera test.
5. In the implementation, how does the performance of the Optimal PID Trading Algorithm compare with other algorithms?
English language quality is fine.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
This is a clearly written and developed paper. It is a plausible representation of market trading and the optimal fine-tuning makes sense. The descriptive validity of such mathematical models is always questionable since they fail to incorporate real market frictions such as the failure of the market to clear (the transactions are too fast and take place on an order by order basis rather than total demand and supply) and short-selling costs (makes the Black-Scholes model fail). However, a model that assumes away these real-life frictions is still useful for understanding price dynamics. Within its limitations, this is an elegant piece of work.
Author Response
We are very grateful for the adequate and professional Reviewer´s opinion.
Reviewer 4 Report
Report on the paper " On a Data-Driven Optimization Approach to the PID Based Algorithmic Trading " submitted in JRFM
Summary of the paper: In this research, an optimal trading algorithm is suggested, built on a creative use of traditional control engineering (CE). The authors discuss feedback control, a key idea in CE, and use it to analyze algorithmic trading (AT). The renowned proportional-integral-derivative (PID) model is used to create the concrete feedback control approach. The adoption of a model-free implementation of the general PID framework is a result of the very volatile nature of contemporary financial markets. For the historical market data, the authors integrate the control theory methods with advanced statistics. The authors obtain an exact log-normal probability distribution function (pdf) corresponding to the precise values corresponding to the stock data that is readily available. The required PID gain optimization can be carried out using the empirical log-normal pdf stated above. To do this, the authors use data-driven optimization techniques and take into account the appropriate Monte Carlo solution process. The Fourier analysis framework is also used to study the optimized PID trading method that the authors suggest. This analogous frequency domain representation uses the "stock market energy" notion, a novel idea in financial engineering. The authors create a Python-based prototype software and execute the suggested PID optimum trading algorithm for evaluation. Finally, the authors use a dataset from the Binance BTC / USDT stock market in conjunction with the associated prototype program. The experimental result demonstrates both the viability of the suggested optimal PID trading scheme and the efficacy of the suggested CE techniques in the contemporary AT.
As mentioned in the report, the English needs a deep improvement.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Concerning my previous report, the authors have considered disregarding some of my suggestions for improvement and corrections. I maintain that they are necessary for the article to be accepted.
The main issues to be solved:
1) For a better understanding of the context and the contributions of the manuscript, the introduction should be changed. Again, I suggest the authors to organize its content as follows:
a) context description, highlighting the issues more relevant for the paper (2 or 3 paragraphs). In the current version, the whole context is unclear from the beginning. Furthermore, in some cases, it is explained mixed with the paper contributions.
b) given such a context, explanation of the motivation of the paper, including the novelties or contributions with respect to the specialized literature (1 or 2 paragraphs).
c) outline of the remainder of the paper (it is actually correct in the current version of the manuscript).
2) In line 113, the order of PID gains should be changed in order to be coherent with the description given, i.e.: K_P, K_I, K_D (proportional, integral, derivative). Notice that you write K_P, K_D, K_I and say that they are proportional, integral and derivative gains, but in reality, taking into account the order in which they are written, they are proportional, derivative and integral gains, respectively. Please correct it. I suggest to change the order of the gains as K_P, K_I, K_D. Check also the vector of gains defined below equation (1).
3) Figures are misplaced in the current version of the paper.
4) Typos:
a) I do not understand the authors' reasoning for capitalizing the term "frequency response" because it is a generic concept in systems engineering. It is recommended to the authors to consult, for example, any book by Aström and Hägglund to verify that for that reason it is not necessary to write it as capitalized.
b) In line 31, “hypothesises” should be replaced by “hypotheses”.
I believe that minor editing of English language are still required.
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
In my previous report, I made five comments. I appreciate that the authors replied to these five comments, but they did not make any changes to the manuscript based on the comments, if I see it correctly.
For example, I still think that based on my first comment, the title of Section 3 should be changed to "Statistical Assumptions on the Stock Market" (or similar), rather than "Advanced Statistical Description of the Stock Market Data".
While I do not expect the authors to address all of my comments, I would hope that they could add some explanations to their manuscript based on my comments, which might help future readers.
English language quality is fine.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
My comment number 2 was again missunderstood. Thus, the authors are recommended to write line 123 of the current version of the manuscript as follows:
"By K_P(·), K_D(·), and K_I(·) we denote here the necessary PID gains for the proportional, derivative, and integral terms of the classic PID regulator scheme"
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
The authors addressed my comments. Therefore, the paper can be accepted, in my opinion.
English language quality is fine.
Author Response
We gratefully acknowledge the positive comments of the Rewiever.
