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 08): Sockets (II)

Market Simulation (Part 08): Sockets (II)

How about creating something practical using sockets? In today's article, we'll start creating a mini-chat. Let's look together at how this is done - it will be very interesting. Please note that the code provided here is for educational purposes only. It should not be used for commercial purposes or in ready-made applications, as it does not provide data transfer security and the content transmitted over the socket can be accessed.
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Market Simulation (Part 09): Sockets (III)

Market Simulation (Part 09): Sockets (III)

Today's article is a continuation of the previous one. We will look at the implementation of an Expert Advisor, focusing mainly on how the server code is executed. The code given in the previous article is not enough to make everything work as expected, so we need to dig a little deeper into it. Therefore, it is necessary to read both articles to better understand what will happen.
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Developing a Replay System (Part 55): Control Module

Developing a Replay System (Part 55): Control Module

In this article, we will implement a control indicator so that it can be integrated into the message system we are developing. Although it is not very difficult, there are some details that need to be understood about the initialization of this module. The material presented here is for educational purposes only. In no way should it be considered as an application for any purpose other than learning and mastering the concepts shown.
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Developing a Replay System (Part 35): Making Adjustments (I)

Developing a Replay System (Part 35): Making Adjustments (I)

Before we can move forward, we need to fix a few things. These are not actually the necessary fixes but rather improvements to the way the class is managed and used. The reason is that failures occurred due to some interaction within the system. Despite attempts to find out the cause of such failures in order to eliminate them, all these attempts were unsuccessful. Some of these cases make no sense, for example, when we use pointers or recursion in C/C++, the program crashes.
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Atmosphere Clouds Model Optimization (ACMO): Practice

Atmosphere Clouds Model Optimization (ACMO): Practice

In this article, we will continue diving into the implementation of the ACMO (Atmospheric Cloud Model Optimization) algorithm. In particular, we will discuss two key aspects: the movement of clouds into low-pressure regions and the rain simulation, including the initialization of droplets and their distribution among clouds. We will also look at other methods that play an important role in managing the state of clouds and ensuring their interaction with the environment.
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Population optimization algorithms: Bacterial Foraging Optimization - Genetic Algorithm (BFO-GA)

Population optimization algorithms: Bacterial Foraging Optimization - Genetic Algorithm (BFO-GA)

The article presents a new approach to solving optimization problems by combining ideas from bacterial foraging optimization (BFO) algorithms and techniques used in the genetic algorithm (GA) into a hybrid BFO-GA algorithm. It uses bacterial swarming to globally search for an optimal solution and genetic operators to refine local optima. Unlike the original BFO, bacteria can now mutate and inherit genes.
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Neuroboids Optimization Algorithm (NOA)

Neuroboids Optimization Algorithm (NOA)

A new bioinspired optimization metaheuristic, NOA (Neuroboids Optimization Algorithm), combines the principles of collective intelligence and neural networks. Unlike conventional methods, the algorithm uses a population of self-learning "neuroboids", each with its own neural network that adapts its search strategy in real time. The article reveals the architecture of the algorithm, the mechanisms of self-learning of agents, and the prospects for applying this hybrid approach to complex optimization problems.
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Feature selection and dimensionality reduction using principal components

Feature selection and dimensionality reduction using principal components

The article delves into the implementation of a modified Forward Selection Component Analysis algorithm, drawing inspiration from the research presented in “Forward Selection Component Analysis: Algorithms and Applications” by Luca Puggini and Sean McLoone.
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Developing a Replay System (Part 39): Paving the Path (III)

Developing a Replay System (Part 39): Paving the Path (III)

Before we proceed to the second stage of development, we need to revise some ideas. Do you know how to make MQL5 do what you need? Have you ever tried to go beyond what is contained in the documentation? If not, then get ready. Because we will be doing something that most people don't normally do.
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Developing a Replay System (Part 41): Starting the second phase (II)

Developing a Replay System (Part 41): Starting the second phase (II)

If everything seemed right to you up to this point, it means you're not really thinking about the long term, when you start developing applications. Over time you will no longer need to program new applications, you will just have to make them work together. So let's see how to finish assembling the mouse indicator.
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Developing a Replay System (Part 34): Order System (III)

Developing a Replay System (Part 34): Order System (III)

In this article, we will complete the first phase of construction. Although this part is fairly quick to complete, I will cover details that were not discussed previously. I will explain some points that many do not understand. Do you know why you have to press the Shift or Ctrl key?
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Central Force Optimization (CFO) algorithm

Central Force Optimization (CFO) algorithm

The article presents the Central Force Optimization (CFO) algorithm inspired by the laws of gravity. It explores how principles of physical attraction can solve optimization problems where "heavier" solutions attract less successful counterparts.
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Stepwise feature selection in MQL5

Stepwise feature selection in MQL5

In this article, we introduce a modified version of stepwise feature selection, implemented in MQL5. This approach is based on the techniques outlined in Modern Data Mining Algorithms in C++ and CUDA C by Timothy Masters.
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Implementing Practical Modules from Other Languages in MQL5 (Part 06): Python-Like File IO operations in MQL5

Implementing Practical Modules from Other Languages in MQL5 (Part 06): Python-Like File IO operations in MQL5

This article shows how to simplify complex MQL5 file operations by building a Python-style interface for effortless reading and writing. It explains how to recreate Python’s intuitive file-handling patterns through custom functions and classes. The result is a cleaner, more reliable approach to MQL5 file I/O.
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Building Volatility models in MQL5 (Part I): The Initial Implementation

Building Volatility models in MQL5 (Part I): The Initial Implementation

In this article, we present an MQL5 library for modeling volatility, designed to function similarly to Python's arch package. The library currently supports the specification of common conditional mean (HAR, AR, Constant Mean, Zero Mean) and conditional volatility (Constant Variance, ARCH, GARCH) models.
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From Novice to Expert: Animated News Headline Using MQL5 (V)—Event Reminder System

From Novice to Expert: Animated News Headline Using MQL5 (V)—Event Reminder System

In this discussion, we’ll explore additional advancements as we integrate refined event‑alerting logic for the economic calendar events displayed by the News Headline EA. This enhancement is critical—it ensures users receive timely notifications a short time before key upcoming events. Join this discussion to discover more.
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Forex Arbitrage Trading: Relationship Assessment Panel

Forex Arbitrage Trading: Relationship Assessment Panel

This article presents the development of an arbitrage analysis panel in MQL5. How to get fair exchange rates on Forex in different ways? Create an indicator to obtain deviations of market prices from fair exchange rates, as well as to assess the benefits of arbitrage ways of exchanging one currency for another (as in triangular arbitrage).
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MQL5 Wizard Techniques you should know (Part 29): Continuation on Learning Rates with MLPs

MQL5 Wizard Techniques you should know (Part 29): Continuation on Learning Rates with MLPs

We wrap up our look at learning rate sensitivity to the performance of Expert Advisors by primarily examining the Adaptive Learning Rates. These learning rates aim to be customized for each parameter in a layer during the training process and so we assess potential benefits vs the expected performance toll.
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Population optimization algorithms: Resistance to getting stuck in local extrema (Part I)

Population optimization algorithms: Resistance to getting stuck in local extrema (Part I)

This article presents a unique 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. Working in this direction will provide further insight into which specific algorithms can successfully continue their search using coordinates set by the user as a starting point, and what factors influence their success.
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Developing a Replay System (Part 56): Adapting the Modules

Developing a Replay System (Part 56): Adapting the Modules

Although the modules already interact with each other properly, an error occurs when trying to use the mouse pointer in the replay service. We need to fix this before moving on to the next step. Additionally, we will fix an issue in the mouse indicator code. So this version will be finally stable and properly polished.
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Developing a Replay System (Part 63): Playing the service (IV)

Developing a Replay System (Part 63): Playing the service (IV)

In this article, we will finally solve the problems with the simulation of ticks on a one-minute bar so that they can coexist with real ticks. This will help us avoid problems in the future. The material presented here is for educational 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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MQL5 Trading Toolkit (Part 7): Expanding the History Management EX5 Library with the Last Canceled Pending Order Functions

MQL5 Trading Toolkit (Part 7): Expanding the History Management EX5 Library with the Last Canceled Pending Order Functions

Learn how to complete the creation of the final module in the History Manager EX5 library, focusing on the functions responsible for handling the most recently canceled pending order. This will provide you with the tools to efficiently retrieve and store key details related to canceled pending orders with MQL5.
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Developing a Replay System (Part 58): Returning to Work on the Service

Developing a Replay System (Part 58): Returning to Work on the Service

After a break in development and improvement of the service used for replay/simulator, we are resuming work on it. Now that we've abandoned the use of resources like terminal globals, we'll have to completely restructure some parts of it. Don't worry, this process will be explained in detail so that everyone can follow the development of our service.
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Python-MetaTrader 5 Strategy Tester (Part 02): Dealing with Bars, Ticks, and Overloading Built-in Functions in a Simulator

Python-MetaTrader 5 Strategy Tester (Part 02): Dealing with Bars, Ticks, and Overloading Built-in Functions in a Simulator

In this article, we introduce functions similar to those provided by the Python-MetaTrader 5 module, providing a simulator with a familiar interface and a custom way of handling bars and ticks internally.
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MQL5 Wizard Techniques you should know (Part 30): Spotlight on Batch-Normalization in Machine Learning

MQL5 Wizard Techniques you should know (Part 30): Spotlight on Batch-Normalization in Machine Learning

Batch normalization is the pre-processing of data before it is fed into a machine learning algorithm, like a neural network. This is always done while being mindful of the type of Activation to be used by the algorithm. We therefore explore the different approaches that one can take in reaping the benefits of this, with the help of a wizard assembled Expert Advisor.
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Market Positioning Codex for VGT with Kendall's Tau and Distance Correlation

Market Positioning Codex for VGT with Kendall's Tau and Distance Correlation

In this article, we look to explore how a complimentary indicator pairing can be used to analyze the recent 5-year history of Vanguard Information Technology Index Fund ETF. By considering two options of algorithms, Kendall’s Tau and Distance-Correlation, we look to select not just an ideal indicator pair for trading the VGT, but also suitable signal-pattern pairings of these two indicators.
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Implementing Practical Modules from Other Languages in MQL5 (Part 05): The Logging module from Python, Log Like a Pro

Implementing Practical Modules from Other Languages in MQL5 (Part 05): The Logging module from Python, Log Like a Pro

Integrating Python's logging module with MQL5 empowers traders with a systematic logging approach, simplifying the process of monitoring, debugging, and documenting trading activities. This article explains the adaptation process, offering traders a powerful tool for maintaining clarity and organization in trading software development.
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Implementation of a table model in MQL5: Applying the MVC concept

Implementation of a table model in MQL5: Applying the MVC concept

In this article, we look at the process of developing a table model in MQL5 using the MVC (Model-View-Controller) architectural pattern to separate data logic, presentation, and control, enabling structured, flexible, and scalable code. We consider implementation of classes for building a table model, including the use of linked lists for storing data.
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From Novice to Expert: Statistical Validation of Supply and Demand Zones

From Novice to Expert: Statistical Validation of Supply and Demand Zones

Today, we uncover the often overlooked statistical foundation behind supply and demand trading strategies. By combining MQL5 with Python through a Jupyter Notebook workflow, we conduct a structured, data-driven investigation aimed at transforming visual market assumptions into measurable insights. This article covers the complete research process, including data collection, Python-based statistical analysis, algorithm design, testing, and final conclusions. To explore the methodology and findings in detail, read the full article.
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Statistical Arbitrage Through Cointegrated Stocks (Part 10): Detecting Structural Breaks

Statistical Arbitrage Through Cointegrated Stocks (Part 10): Detecting Structural Breaks

This article presents the Chow test for detecting structural breaks in pair relationships and the application of the Cumulative Sum of Squares - CUSUM - for structural breaks monitoring and early detection. The article uses the Nvidia/Intel partnership announcement and the US Gov foreign trade tariff announcement as examples of slope inversion and intercept shift, respectively. Python scripts for all the tests are provided.
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Larry Williams Market Secrets (Part 7): An Empirical Study of the Trade Day of the Week Concept

Larry Williams Market Secrets (Part 7): An Empirical Study of the Trade Day of the Week Concept

An empirical study of Larry Williams’ Trade Day of the Week concept, showing how time-based market bias can be measured, tested, and applied using MQL5. This article presents a practical framework for analyzing win rates and performance across trading days to improve short-term trading systems.
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MQL5 Trading Tools (Part 14): Pixel-Perfect Scrollable Text Canvas with Antialiasing and Rounded Scrollbar

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.
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Tracking Account Dynamics: Balance, Equity, and Floating P/L Visualization in MQL5

Tracking Account Dynamics: Balance, Equity, and Floating P/L Visualization in MQL5

Create a custom MT5 indicator that processes the entire deal history and plots starting balance, balance, equity, and floating P/L as continuous curves. It updates per bar, aggregates positions across symbols, and avoids external dependencies through local caching. Use it to inspect equity–balance divergence, realized vs. unrealized results, and the timing of risk deployment.
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Neuroboids Optimization Algorithm 2 (NOA2)

Neuroboids Optimization Algorithm 2 (NOA2)

The new proprietary optimization algorithm NOA2 (Neuroboids Optimization Algorithm 2) combines the principles of swarm intelligence with neural control. NOA2 combines the mechanics of a neuroboid swarm with an adaptive neural system that allows agents to self-correct their behavior while searching for the optimum. The algorithm is under active development and demonstrates potential for solving complex optimization problems.
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Market Simulation (Part 10): Sockets (IV)

Market Simulation (Part 10): Sockets (IV)

In this article, we'll look at what you need to do to start using Excel to manage MetaTrader 5, but in a very interesting way. To do this, we will use an Excel add-in to avoid using built-in VBA. If you don't know what add-in is meant, read this article and learn how to program in Python directly in Excel.
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From Novice to Expert: Statistical Validation of Supply and Demand Zones

From Novice to Expert: Statistical Validation of Supply and Demand Zones

Today, we uncover the often overlooked statistical foundation behind supply and demand trading strategies. By combining MQL5 with Python through a Jupyter Notebook workflow, we conduct a structured, data-driven investigation aimed at transforming visual market assumptions into measurable insights. This article covers the complete research process, including data collection, Python-based statistical analysis, algorithm design, testing, and final conclusions. To explore the methodology and findings in detail, read the full article.