Articles on data analysis and statistics in MQL5

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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.

Read about the fuzzy logic, digital filters, market profile, Kohonen maps, neural gas and many other tools that can be used for trading.

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Market Simulation (Part 01): Cross Orders (I)

Market Simulation (Part 01): Cross Orders (I)

Today we will begin the second stage, where we will look at the market replay/simulation system. First, we will show a possible solution for cross orders. I will show you the solution, but it is not final yet. It will be a possible solution to a problem that we will need to solve in the near future.
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Neural networks made easy (Part 40): Using Go-Explore on large amounts of data

Neural networks made easy (Part 40): Using Go-Explore on large amounts of data

This article discusses the use of the Go-Explore algorithm over a long training period, since the random action selection strategy may not lead to a profitable pass as training time increases.
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3D Visualization Without External Libraries: How MetaTrader 5 Reveals Optimization Results via MQL5 + DX11

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.
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Population optimization algorithms: Evolution Strategies, (μ,λ)-ES and (μ+λ)-ES

Population optimization algorithms: Evolution Strategies, (μ,λ)-ES and (μ+λ)-ES

The article considers a group of optimization algorithms known as Evolution Strategies (ES). They are among the very first population algorithms to use evolutionary principles for finding optimal solutions. We will implement changes to the conventional ES variants and revise the test function and test stand methodology for the algorithms.
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Blood inheritance optimization (BIO)

Blood inheritance optimization (BIO)

I present to you my new population optimization algorithm - Blood Inheritance Optimization (BIO), inspired by the human blood group inheritance system. In this algorithm, each solution has its own "blood type" that determines the way it evolves. Just as in nature where a child's blood type is inherited according to specific rules, in BIO new solutions acquire their characteristics through a system of inheritance and mutations.
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Price Action Analysis Toolkit Development (Part 80): Building a History Navigator for MetaTrader 5

Price Action Analysis Toolkit Development (Part 80): Building a History Navigator for MetaTrader 5

We implement a History Navigator for MetaTrader 5 that jumps the chart to an exact historical period by date and time. The dialog validates inputs, converts them to datetime, and searches bar times with a binary-search routine before centering the selected candle. The navigation logic is separated from chart control, improving testability and maintenance, and a one-click return restores the live market view.
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Developing a Replay System — Market simulation (Part 23): FOREX (IV)

Developing a Replay System — Market simulation (Part 23): FOREX (IV)

Now the creation occurs at the same point where we converted ticks into bars. This way, if something goes wrong during the conversion process, we will immediately notice the error. This is because the same code that places 1-minute bars on the chart during fast forwarding is also used for the positioning system to place bars during normal performance. In other words, the code that is responsible for this task is not duplicated anywhere else. This way we get a much better system for both maintenance and improvement.
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Developing a Replay System — Market simulation (Part 22): FOREX (III)

Developing a Replay System — Market simulation (Part 22): FOREX (III)

Although this is the third article on this topic, I must explain for those who have not yet understood the difference between the stock market and the foreign exchange market: the big difference is that in the Forex there is no, or rather, we are not given information about some points that actually occurred during the course of trading.
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Introduction to MQL5 (Part 31): Mastering API and WebRequest Function in MQL5 (V)

Introduction to MQL5 (Part 31): Mastering API and WebRequest Function in MQL5 (V)

Learn how to use WebRequest and external API calls to retrieve recent candle data, convert each value into a usable type, and save the information neatly in a table format. This step lays the groundwork for building an indicator that visualizes the data in candle format.
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Neural networks made easy (Part 41): Hierarchical models

Neural networks made easy (Part 41): Hierarchical models

The article describes hierarchical training models that offer an effective approach to solving complex machine learning problems. Hierarchical models consist of several levels, each of which is responsible for different aspects of the task.
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How to implement AutoARIMA forecasting in MQL5

How to implement AutoARIMA forecasting in MQL5

This article presents an MQL5 implementation of AutoARIMA that builds ARIMA models without manual tuning. It estimates d via a variance-based heuristic, fits ARMA(p,q) by gradient optimization with Adam, and selects p and q using AICc. The code returns a one-step-ahead price forecast by differencing, model estimation, and integration back to price level, ready to call on a Close series.
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Big Bang - Big Crunch (BBBC) algorithm

Big Bang - Big Crunch (BBBC) algorithm

The article presents the Big Bang - Big Crunch method, which has two key phases: cyclic generation of random points and their compression to the optimal solution. This approach combines exploration and refinement, allowing us to gradually find better solutions and open up new optimization opportunities.
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Statistical Arbitrage Through Cointegrated Stocks (Part 5): Screening

Statistical Arbitrage Through Cointegrated Stocks (Part 5): Screening

This article proposes an asset screening process for a statistical arbitrage trading strategy through cointegrated stocks. The system starts with the regular filtering by economic factors, like asset sector and industry, and finishes with a list of criteria for a scoring system. For each statistical test used in the screening, a respective Python class was developed: Pearson correlation, Engle-Granger cointegration, Johansen cointegration, and ADF/KPSS stationarity. These Python classes are provided along with a personal note from the author about the use of AI assistants for software development.
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Data Science and ML (Part 35): NumPy in MQL5 – The Art of Making Complex Algorithms with Less Code

Data Science and ML (Part 35): NumPy in MQL5 – The Art of Making Complex Algorithms with Less Code

NumPy library is powering almost all the machine learning algorithms to the core in Python programming language, In this article we are going to implement a similar module which has a collection of all the complex code to aid us in building sophisticated models and algorithms of any kind.
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Developing a Replay System (Part 37): Paving the Path (I)

Developing a Replay System (Part 37): Paving the Path (I)

In this article, we will finally begin to do what we wanted to do much earlier. However, due to the lack of "solid ground", I did not feel confident to present this part publicly. Now I have the basis to do this. I suggest that you focus as much as possible on understanding the content of this article. I mean not simply reading it. I want to emphasize that if you do not understand this article, you can completely give up hope of understanding the content of the following ones.
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Data Science and ML (Part 39): News + Artificial Intelligence, Would You Bet on it?

Data Science and ML (Part 39): News + Artificial Intelligence, Would You Bet on it?

News drives the financial markets, especially major releases like Non-Farm Payrolls (NFPs). We've all witnessed how a single headline can trigger sharp price movements. In this article, we dive into the powerful intersection of news data and Artificial Intelligence.
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Developing a Replay System (Part 75): New Chart Trade (II)

Developing a Replay System (Part 75): New Chart Trade (II)

In this article, we will talk about the C_ChartFloatingRAD class. This is what makes Chart Trade work. However, the explanation does not end there. We will complete it in the next article, as the content of this article is quite extensive and requires deep understanding. 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.
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Developing a Replay System (Part 51): Things Get Complicated (III)

Developing a Replay System (Part 51): Things Get Complicated (III)

In this article, we will look into one of the most difficult issues in the field of MQL5 programming: how to correctly obtain a chart ID, and why objects are sometimes not plotted on the chart. The materials presented here are for didactic purposes only. Under no circumstances should the application be viewed for any purpose other than to learn and master the concepts presented.
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Population optimization algorithms: Bird Swarm Algorithm (BSA)

Population optimization algorithms: Bird Swarm Algorithm (BSA)

The article explores the bird swarm-based algorithm (BSA) inspired by the collective flocking interactions of birds in nature. The different search strategies of individuals in BSA, including switching between flight, vigilance and foraging behavior, make this algorithm multifaceted. It uses the principles of bird flocking, communication, adaptability, leading and following to efficiently find optimal solutions.
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Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (I)

Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (I)

This discussion delves into the challenges encountered when working with large codebases. We will explore the best practices for code organization in MQL5 and implement a practical approach to enhance the readability and scalability of our Trading Administrator Panel source code. Additionally, we aim to develop reusable code components that can potentially benefit other developers in their algorithm development. Read on and join the conversation.
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Developing a Replay System (Part 54): The Birth of the First Module

Developing a Replay System (Part 54): The Birth of the First Module

In this article, we will look at how to put together the first of a number of truly functional modules for use in the replay/simulator system that will also be of general purpose to serve other purposes. We are talking about the mouse module.
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Population optimization algorithms: Simulated Annealing (SA) algorithm. Part I

Population optimization algorithms: Simulated Annealing (SA) algorithm. Part I

The Simulated Annealing algorithm is a metaheuristic inspired by the metal annealing process. In the article, we will conduct a thorough analysis of the algorithm and debunk a number of common beliefs and myths surrounding this widely known optimization method. The second part of the article will consider the custom Simulated Isotropic Annealing (SIA) algorithm.
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Integrating MQL5 with data processing packages (Part 4): Big Data Handling

Integrating MQL5 with data processing packages (Part 4): Big Data Handling

Exploring advanced techniques to integrate MQL5 with powerful data processing tools, this part focuses on efficient handling of big data to enhance trading analysis and decision-making.
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Chaos Game Optimization (CGO)

Chaos Game Optimization (CGO)

The article presents a new metaheuristic algorithm, Chaos Game Optimization (CGO), which demonstrates a unique ability to maintain high efficiency when dealing with high-dimensional problems. Unlike most optimization algorithms, CGO not only does not lose, but sometimes even increases performance when scaling a problem, which is its key feature.
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Developing a Replay System — Market simulation (Part 19): Necessary adjustments

Developing a Replay System — Market simulation (Part 19): Necessary adjustments

Here we will prepare the ground so that if we need to add new functions to the code, this will happen smoothly and easily. The current code cannot yet cover or handle some of the things that will be necessary to make meaningful progress. We need everything to be structured in order to enable the implementation of certain things with the minimal effort. If we do everything correctly, we can get a truly universal system that can very easily adapt to any situation that needs to be handled.
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Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (II): Modularization

Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (II): Modularization

In this discussion, we take a step further in breaking down our MQL5 program into smaller, more manageable modules. These modular components will then be integrated into the main program, enhancing its organization and maintainability. This approach simplifies the structure of our main program and makes the individual components reusable in other Expert Advisors (EAs) and indicator developments. By adopting this modular design, we create a solid foundation for future enhancements, benefiting both our project and the broader developer community.
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Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (III): Communication Module

Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (III): Communication Module

Join us for an in-depth discussion on the latest advancements in MQL5 interface design as we unveil the redesigned Communications Panel and continue our series on building the New Admin Panel using modularization principles. We'll develop the CommunicationsDialog class step by step, thoroughly explaining how to inherit it from the Dialog class. Additionally, we'll leverage arrays and ListView class in our development. Gain actionable insights to elevate your MQL5 development skills—read through the article and join the discussion in the comments section!
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Integrating MQL5 with Data Processing Packages (Part 7): Building Multi-Agent Environments for Cross-Symbol Collaboration

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.
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Feature Engineering With Python And MQL5 (Part II): Angle Of Price

Feature Engineering With Python And MQL5 (Part II): Angle Of Price

There are many posts in the MQL5 Forum asking for help calculating the slope of price changes. This article will demonstrate one possible way of calculating the angle formed by the changes in price in any market you wish to trade. Additionally, we will answer if engineering this new feature is worth the extra effort and time invested. We will explore if the slope of the price can improve any of our AI model's accuracy when forecasting the USDZAR pair on the M1.
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Coral Reefs Optimization (CRO)

Coral Reefs Optimization (CRO)

The article presents a comprehensive analysis of the Coral Reef Optimization (CRO) algorithm, a metaheuristic method inspired by the biological processes of coral reef formation and development. The algorithm models key aspects of coral evolution: broadcast spawning, brooding, larval settlement, asexual reproduction, and competition for limited reef space. Particular attention is paid to the improved version of the algorithm.
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Category Theory in MQL5 (Part 23): A different look at the Double Exponential Moving Average

Category Theory in MQL5 (Part 23): A different look at the Double Exponential Moving Average

In this article we continue with our theme in the last of tackling everyday trading indicators viewed in a ‘new’ light. We are handling horizontal composition of natural transformations for this piece and the best indicator for this, that expands on what we just covered, is the double exponential moving average (DEMA).
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Developing a Replay System (Part 71): Getting the Time Right (IV)

Developing a Replay System (Part 71): Getting the Time Right (IV)

In this article, we will look at how to implement what was shown in the previous article related to our replay/simulation service. As in many other things in life, problems are bound to arise. And this case was no exception. In this article, we continue to improve things. 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.
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Royal Flush Optimization (RFO)

Royal Flush Optimization (RFO)

The original Royal Flush Optimization algorithm offers a new approach to solving optimization problems, replacing the classic binary coding of genetic algorithms with a sector-based approach inspired by poker principles. RFO demonstrates how simplifying basic principles can lead to an efficient and practical optimization method. The article presents a detailed analysis of the algorithm and test results.
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One-Dimensional Singular Spectrum Analysis

One-Dimensional Singular Spectrum Analysis

The article examines the theoretical and practical aspects of the singular spectrum analysis (SSA) method, which is an efficient method of time series analysis that allows one to represent the complex structure of a series as a decomposition into simple components, such as trend, seasonal (periodic) fluctuations and noise.
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Comet Tail Algorithm (CTA)

Comet Tail Algorithm (CTA)

In this article, we will look at the Comet Tail Optimization Algorithm (CTA), which draws inspiration from unique space objects - comets and their impressive tails that form when approaching the Sun. The algorithm is based on the concept of the motion of comets and their tails, and is designed to find optimal solutions in optimization problems.
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Reimagining Classic Strategies (Part 14): Multiple Strategy Analysis

Reimagining Classic Strategies (Part 14): Multiple Strategy Analysis

In this article, we continue our exploration of building an ensemble of trading strategies and using the MT5 genetic optimizer to tune the strategy parameters. Today, we analyzed the data in Python, showing our model could better predict which strategy would outperform, achieving higher accuracy than forecasting market returns directly. However, when we tested our application with its statistical models, our performance levels fell dismally. We subsequently discovered that the genetic optimizer unfortunately favored highly correlated strategies, prompting us to revise our method to keep vote weights fixed and focus optimization on indicator settings instead.
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Artificial Bee Hive Algorithm (ABHA): Tests and results

Artificial Bee Hive Algorithm (ABHA): Tests and results

In this article, we will continue exploring the Artificial Bee Hive Algorithm (ABHA) by diving into the code and considering the remaining methods. As you might remember, each bee in the model is represented as an individual agent whose behavior depends on internal and external information, as well as motivational state. We will test the algorithm on various functions and summarize the results by presenting them in the rating table.
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Singular Spectrum Analysis in MQL5

Singular Spectrum Analysis in MQL5

This article is meant as a guide for those unfamiliar with the concept of Singular Spectrum Analysis and who wish to gain enough understanding to be able to apply the built-in tools available in MQL5.
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Population optimization algorithms: Intelligent Water Drops (IWD) algorithm

Population optimization algorithms: Intelligent Water Drops (IWD) algorithm

The article considers an interesting algorithm derived from inanimate nature - intelligent water drops (IWD) simulating the process of river bed formation. The ideas of this algorithm made it possible to significantly improve the previous leader of the rating - SDS. As usual, the new leader (modified SDSm) can be found in the attachment.
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Data label for time series mining (Part 5):Apply and Test in EA Using Socket

Data label for time series mining (Part 5):Apply and Test in EA Using Socket

This series of articles introduces several time series labeling methods, which can create data that meets most artificial intelligence models, and targeted data labeling according to needs can make the trained artificial intelligence model more in line with the expected design, improve the accuracy of our model, and even help the model make a qualitative leap!