Articles on data analysis and statistics in MQL5
Articles on mathematical models and laws of probability are interesting for many traders. Mathematics is the basis of technical indicators, and statistics is required to analyze trading results and develop strategies.
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Statistical Arbitrage Through Cointegrated Stocks (Part 8): Rolling Windows Eigenvector Comparison for Portfolio Rebalancing
This article proposes using Rolling Windows Eigenvector Comparison for early imbalance diagnostics and portfolio rebalancing in a mean-reversion statistical arbitrage strategy based on cointegrated stocks. It contrasts this technique with traditional In-Sample/Out-of-Sample ADF validation, showing that eigenvector shifts can signal the need for rebalancing even when IS/OOS ADF still indicates a stationary spread. While the method is intended mainly for live trading monitoring, the article concludes that eigenvector comparison could also be integrated into the scoring system—though its actual contribution to performance remains to be tested.
ALGLIB library optimization methods (Part I)
In this article, we will get acquainted with the ALGLIB library optimization methods for MQL5. The article includes simple and clear examples of using ALGLIB to solve optimization problems, which will make mastering the methods as accessible as possible. We will take a detailed look at the connection of such algorithms as BLEIC, L-BFGS and NS, and use them to solve a simple test problem.
Developing a Replay System (Part 44): Chart Trade Project (III)
In the previous article I explained how you can manipulate template data for use in OBJ_CHART. In that article, I only outlined the topic without going into details, since in that version the work was done in a very simplified way. This was done to make it easier to explain the content, because despite the apparent simplicity of many things, some of them were not so obvious, and without understanding the simplest and most basic part, you would not be able to truly understand the entire picture.
Permuting price bars in MQL5
In this article we present an algorithm for permuting price bars and detail how permutation tests can be used to recognize instances where strategy performance has been fabricated to deceive potential buyers of Expert Advisors.
Integrating MQL5 with Data Processing Packages (Part 7): Building Multi-Agent Environments for Cross-Symbol Collaboration
The article presents a complete Python–MQL5 integration for multi‑agent trading: MT5 data ingestion, indicator computation, per‑agent decisions, and a weighted consensus that outputs a single action. Signals are stored to JSON, served by Flask, and consumed by an MQL5 Expert Advisor for execution with position sizing and ATR‑derived SL/TP. Flask routes provide safe lifecycle control and status monitoring.
Population optimization algorithms: Simulated Isotropic Annealing (SIA) algorithm. Part II
The first part was devoted to the well-known and popular algorithm - simulated annealing. We have thoroughly considered its pros and cons. The second part of the article is devoted to the radical transformation of the algorithm, which turns it into a new optimization algorithm - Simulated Isotropic Annealing (SIA).
Statistical Arbitrage Through Cointegrated Stocks (Part 3): Database Setup
This article presents a sample MQL5 Service implementation for updating a newly created database used as source for data analysis and for trading a basket of cointegrated stocks. The rationale behind the database design is explained in detail and the data dictionary is documented for reference. MQL5 and Python scripts are provided for the database creation, schema initialization, and market data insertion.
MQL5 Wizard Techniques you should know (Part 07): Dendrograms
Data classification for purposes of analysis and forecasting is a very diverse arena within machine learning and it features a large number of approaches and methods. This piece looks at one such approach, namely Agglomerative Hierarchical Classification.
Category Theory in MQL5 (Part 6): Monomorphic Pull-Backs and Epimorphic Push-Outs
Category Theory is a diverse and expanding branch of Mathematics which is only recently getting some coverage in the MQL5 community. These series of articles look to explore and examine some of its concepts & axioms with the overall goal of establishing an open library that provides insight while also hopefully furthering the use of this remarkable field in Traders' strategy development.
Developing a Replay System (Part 66): Playing the service (VII)
In this article, we will implement the first solution that will allow us to determine when a new bar may appear on the chart. This solution is applicable in a wide variety of situations. Understanding its development will help you grasp several important aspects. The content presented here is intended solely for educational purposes. Under no circumstances should the application be viewed for any purpose other than to learn and master the concepts presented.
Creating a Trading Administrator Panel in MQL5 (Part XI): Modern feature communications interface (I)
Today, we are focusing on the enhancement of the Communications Panel messaging interface to align with the standards of modern, high-performing communication applications. This improvement will be achieved by updating the CommunicationsDialog class. Join us in this article and discussion as we explore key insights and outline the next steps in advancing interface programming using MQL5.
3D Visualization Without External Libraries: How MetaTrader 5 Reveals Optimization Results via MQL5 + DX11
The article describes the practical application of DirectX 11 and built-in MQL5 tools for creating 3D visualizations and interactive interfaces in MetaTrader 5. The focus is on cognitive efficiency - the ability of 3D charts and guided scenes to help in understanding optimization data, liquidity clusters, and multi-dimensional trading scenarios. The basics of the DX pipeline, working with shaders, binding mouse and keyboard events, and objective technological limitations are discussed in detail. The article is intended for MQL5 developers and algorithmic traders who are ready to transform strategy metrics into understandable 3D analytical landscapes, where the visual layer accelerates decision-making.
Low-Frequency Quantitative Strategies in MetaTrader 5 (Part 3): A Regime-Adaptive Mean-Reversion Swing Trading System
The article describes and codes MR Swing in MQL5, a mean‑reversion swing approach that combines a 200‑day hysteresis channel with Value Charts, DVO, and SVAPO. We document entry/exit rules for bull and bear regimes and show five‑year backtests on six high‑liquidity Nasdaq stocks. The complete EA code and backtest configurations are provided for reproducibility.
Market Simulation (Part 16): Sockets (X)
We are close to completing this challenge. However, before we begin, I want you to try to understand these two articles—this one and the previous one. That way, you will truly understand the next article, in which I will cover exclusively the part related to MQL5 programming. But I will also try to make it understandable. If you do not understand these last two articles, it will be difficult for you to understand the next one, because the material accumulates. The more things there are to do, the more you need to create and understand in order to achieve the goal.
Developing a Replay System (Part 49): Things Get Complicated (I)
In this article, we'll complicate things a little. Using what was shown in the previous articles, we will start to open up the template file so that the user can use their own template. However, I will be making changes gradually, as I will also be refining the indicator to reduce the load on MetaTrader 5.
Matrix Factorization: The Basics
Since the goal here is didactic, we will proceed as simply as possible. That is, we will implement only what we need: matrix multiplication. You will see today that this is enough to simulate matrix-scalar multiplication. The most significant difficulty that many people encounter when implementing code using matrix factorization is this: unlike scalar factorization, where in almost all cases the order of the factors does not change the result, this is not the case when using matrices.
Visualizing deals on a chart (Part 1): Selecting a period for analysis
Here we are going to develop a script from scratch that simplifies unloading print screens of deals for analyzing trading entries. All the necessary information on a single deal is to be conveniently displayed on one chart with the ability to draw different timeframes.
MQL5 Trading Tools (Part 24): Depth-Perception Upgrades with 3D Curves, Pan Mode, and ViewCube Navigation
In this article, we enhance the 3D binomial distribution graphing tool in MQL5 by adding a segmented 3D curve for improved depth perception of the probability mass function, integrating pan mode for view target shifting, and implementing an interactive view cube with hover zones and animations for quick orientation changes. We incorporate clickable sub-zones on the view cube for faces, edges, and corners to animate camera transitions to standard views, while maintaining switchable 2D/3D modes, real-time updates, and customizable parameters for immersive probabilistic analysis in trading.
Developing a Replay System — Market simulation (Part 07): First improvements (II)
In the previous article, we made some fixes and added tests to our replication system to ensure the best possible stability. We also started creating and using a configuration file for this system.
Developing a Replay System — Market simulation (Part 16): New class system
We need to organize our work better. The code is growing, and if this is not done now, then it will become impossible. Let's divide and conquer. MQL5 allows the use of classes which will assist in implementing this task, but for this we need to have some knowledge about classes. Probably the thing that confuses beginners the most is inheritance. In this article, we will look at how to use these mechanisms in a practical and simple way.
Gaussian Processes in Machine Learning: Regression Model in MQL5
We will review the basics of Gaussian processes (GP) as a probabilistic machine learning model and demonstrate its application to regression problems using synthetic data.
Population optimization algorithms: Resistance to getting stuck in local extrema (Part II)
We continue our experiment that aims to examine the behavior of population optimization algorithms in the context of their ability to efficiently escape local minima when population diversity is low and reach global maxima. Research results are provided.
Bivariate Copulae in MQL5 (Part 2): Implementing Archimedean copulae in MQL5
In the second installment of the series, we discuss the properties of bivariate Archimedean copulae and their implementation in MQL5. We also explore applying copulae to the development of a simple pairs trading strategy.
MQL5 Wizard Techniques you should know (Part 52): Accelerator Oscillator
The Accelerator Oscillator is another Bill Williams Indicator that tracks price momentum's acceleration and not just its pace. Although much like the Awesome oscillator we reviewed in a recent article, it seeks to avoid the lagging effects by focusing more on acceleration as opposed to just speed. We examine as always what patterns we can get from this and also what significance each could have in trading via a wizard assembled Expert Advisor.
Resampling techniques for prediction and classification assessment in MQL5
In this article, we will explore and implement, methods for assessing model quality that utilize a single dataset as both training and validation sets.
MQL5 Trading Tools (Part 14): Pixel-Perfect Scrollable Text Canvas with Antialiasing and Rounded Scrollbar
In this article, we enhance the canvas-based price dashboard in MQL5 by adding a pixel-perfect scrollable text panel for usage guides, overcoming native scrolling limitations through custom antialiasing and a rounded scrollbar design with hover-expand functionality. The text panel supports themed backgrounds with opacity, dynamic line wrapping for content like instructions and contacts, and interactive navigation via up/down buttons, slider dragging, and mouse wheel scrolling within the body area.
Developing a Replay System (Part 72): An Unusual Communication (I)
What we create today will be difficult to understand. Therefore, in this article I will only talk about the initial stage. Please read this article carefully, it is an important prerequisite before we proceed to the next step. The purpose of this material is purely didactic as we will only study and master the presented concepts, without practical application.
Population optimization algorithms: Boids Algorithm
The article considers Boids algorithm based on unique examples of animal flocking behavior. In turn, the Boids algorithm serves as the basis for the creation of the whole class of algorithms united under the name "Swarm Intelligence".
Data Science and ML (Part 36): Dealing with Biased Financial Markets
Financial markets are not perfectly balanced. Some markets are bullish, some are bearish, and some exhibit some ranging behaviors indicating uncertainty in either direction, this unbalanced information when used to train machine learning models can be misleading as the markets change frequently. In this article, we are going to discuss several ways to tackle this issue.
Statistical Arbitrage Through Cointegrated Stocks (Final): Data Analysis with Specialized Database
The article shows how to pair SQLite (OLTP) with DuckDB (OLAP) for statistical arbitrage data processing. DuckDB’s columnar engine, ASOF JOIN, and array functions accelerate core tasks such as quote–trade alignment and RWEC, with measured speedups from 2x to 23x versus SQLite on larger inputs. You get simpler queries and faster analytics while keeping trade execution in SQLite.
Integrating MQL5 with Data Processing Packages (Part 6): Merging Market Feedback with Model Adaptation
In this part, we focus on how to merge real-time market feedback—such as live trade outcomes, volatility changes, and liquidity shifts—with adaptive model learning to maintain a responsive and self-improving trading system.
Developing a Replay System (Part 47): Chart Trade Project (VI)
Finally, our Chart Trade indicator starts interacting with the EA, allowing information to be transferred interactively. Therefore, in this article, we will improve the indicator, making it functional enough to be used together with any EA. This will allow us to access the Chart Trade indicator and work with it as if it were actually connected with an EA. But we will do it in a much more interesting way than before.
Capital management in trading and the trader's home accounting program with a database
How can a trader manage capital? How can a trader and investor keep track of expenses, income, assets, and liabilities? I am not just going to introduce you to accounting software; I am going to show you a tool that might become your reliable financial navigator in the stormy sea of trading.
Self Optimizing Expert Advisors in MQL5 (Part 12): Building Linear Classifiers Using Matrix Factorization
This article explores the powerful role of matrix factorization in algorithmic trading, specifically within MQL5 applications. From regression models to multi-target classifiers, we walk through practical examples that demonstrate how easily these techniques can be integrated using built-in MQL5 functions. Whether you're predicting price direction or modeling indicator behavior, this guide lays a strong foundation for building intelligent trading systems using matrix methods.
Integrating Computer Vision into Trading in MQL5 (Part 2): Extending the Architecture to 2D RGB Image Analysis
Computer vision for trading: how it works and how to develop it step by step. We create an algorithm for recognition of RGB images of price charts using the attention mechanism and a bidirectional LSTM layer. As a result, we obtain a working model for forecasting the EURUSD price with the accuracy of up to 55% in the validation section.
Implementing Practical Modules from Other Languages in MQL5 (Part 04): time, date, and datetime modules from Python
Unlike MQL5, Python programming language offers control and flexibility when it comes to dealing with and manipulating time. In this article, we will implement similar modules for better handling of dates and time in MQL5 as in Python.
MQL5 Wizard Techniques you should know (Part 55): SAC with Prioritized Experience Replay
Replay buffers in Reinforcement Learning are particularly important with off-policy algorithms like DQN or SAC. This then puts the spotlight on the sampling process of this memory-buffer. While default options with SAC, for instance, use random selection from this buffer, Prioritized Experience Replay buffers fine tune this by sampling from the buffer based on a TD-score. We review the importance of Reinforcement Learning, and, as always, examine just this hypothesis (not the cross-validation) in a wizard assembled Expert Advisor.
Where should your stop-loss really sit? An MAE/MFE excursion analyzer in MQL5
Stop-loss and take-profit placement is usually the least-measured decision in a trading system. This Expert Advisor reads your closed history, replays M1 price between each entry and exit to measure Maximum Adverse and Favorable Excursion per trade, and splits winners from losers. From the distributions and trade efficiency it derives data-driven stop and target levels - measured from your own account, not a rule of thumb. Analysis only; it does not trade.
Developing a Replay System (Part 62): Playing the service (III)
In this article, we will begin to address the issue of tick excess that can impact application performance when using real data. This excess often interferes with the correct timing required to construct a one-minute bar in the appropriate window.
Analyzing binary code of prices on the exchange (Part II): Converting to BIP39 and writing GPT model
Continuing tries to decipher price movements... What about linguistic analysis of the "market dictionary" that we get by converting the binary price code to BIP39? In this article, we will delve into an innovative approach to exchange data analysis and consider how modern natural language processing techniques can be applied to the market language.