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 07): Sockets (I)

Market Simulation (Part 07): Sockets (I)

Sockets. Do you know what they are for or how to use them in MetaTrader 5? If the answer is no, let's start by studying them. In today's article, we'll cover the basics. Since there are several ways to do the same thing, and we are always interested in the result, I want to show that there is indeed a simple way to transfer data from MetaTrader 5 to other programs, such as Excel. However, the main idea is not to transfer data from MetaTrader 5 to Excel, but the opposite, that is, to transfer data from Excel or any other program to MetaTrader 5.
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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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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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MQL5 Wizard Techniques you should know (Part 20): Symbolic Regression

MQL5 Wizard Techniques you should know (Part 20): Symbolic Regression

Symbolic Regression is a form of regression that starts with minimal to no assumptions on what the underlying model that maps the sets of data under study would look like. Even though it can be implemented by Bayesian Methods or Neural Networks, we look at how an implementation with Genetic Algorithms can help customize an expert signal class usable in the MQL5 wizard.
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MQL5 Wizard Techniques you should know (Part 33): Gaussian Process Kernels

MQL5 Wizard Techniques you should know (Part 33): Gaussian Process Kernels

Gaussian Process Kernels are the covariance function of the Normal Distribution that could play a role in forecasting. We explore this unique algorithm in a custom signal class of MQL5 to see if it could be put to use as a prime entry and exit signal.
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News Trading Made Easy (Part 4): Performance Enhancement

News Trading Made Easy (Part 4): Performance Enhancement

This article will dive into methods to improve the expert's runtime in the strategy tester, the code will be written to divide news event times into hourly categories. These news event times will be accessed within their specified hour. This ensures that the EA can efficiently manage event-driven trades in both high and low-volatility environments.
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Developing a Replay System (Part 65): Playing the service (VI)

Developing a Replay System (Part 65): Playing the service (VI)

In this article, we will look at how to implement and solve the mouse pointer issue when using it in conjunction with a replay/simulation application. 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 52): Things Get Complicated (IV)

Developing a Replay System (Part 52): Things Get Complicated (IV)

In this article, we will change the mouse pointer to enable the interaction with the control indicator to ensure reliable and stable operation.
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Bivariate Copulae in MQL5 (Part 1): Implementing Gaussian and Student's t-Copulae for Dependency Modeling

Bivariate Copulae in MQL5 (Part 1): Implementing Gaussian and Student's t-Copulae for Dependency Modeling

This is the first part of an article series presenting the implementation of bivariate copulae in MQL5. This article presents code implementing Gaussian and Student's t-copulae. It also delves into the fundamentals of statistical copulae and related topics. The code is based on the Arbitragelab Python package by Hudson and Thames.
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Category Theory in MQL5 (Part 11): Graphs

Category Theory in MQL5 (Part 11): Graphs

This article is a continuation in a series that look at Category Theory implementation in MQL5. In here we examine how Graph-Theory could be integrated with monoids and other data structures when developing a close-out strategy to a trading system.
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Multiple Symbol Analysis With Python And MQL5 (Part II): Principal Components Analysis For Portfolio Optimization

Multiple Symbol Analysis With Python And MQL5 (Part II): Principal Components Analysis For Portfolio Optimization

Managing trading account risk is a challenge for all traders. How can we develop trading applications that dynamically learn high, medium, and low-risk modes for various symbols in MetaTrader 5? By using PCA, we gain better control over portfolio variance. I’ll demonstrate how to create applications that learn these three risk modes from market data fetched from MetaTrader 5.
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Market Simulation (Part 03): A Matter of Performance

Market Simulation (Part 03): A Matter of Performance

Often we have to take a step back and then move forward. In this article, we will show all the changes necessary to ensure that the Mouse and Chart Trade indicators do not break. As a bonus, we'll also cover other changes that have occurred in other header files that will be widely used in the future.
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Battle Royale Optimizer (BRO)

Battle Royale Optimizer (BRO)

The article explores the Battle Royale Optimizer algorithm — a metaheuristic in which solutions compete with their nearest neighbors, accumulate “damage,” are replaced when a threshold is exceeded, and periodically shrink the search space around the current best solution. It presents both pseudocode and an MQL5 implementation of the CAOBRO class, including neighbor search, movement toward the best solution, and an adaptive delta interval. Test results on the Hilly, Forest, and Megacity functions highlight the strengths and limitations of the approach. The reader is provided with a ready-to-use foundation for experimentation and tuning key parameters such as popSize and maxDamage.
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Population optimization algorithms: Binary Genetic Algorithm (BGA). Part I

Population optimization algorithms: Binary Genetic Algorithm (BGA). Part I

In this article, we will explore various methods used in binary genetic and other population algorithms. We will look at the main components of the algorithm, such as selection, crossover and mutation, and their impact on the optimization. In addition, we will study data presentation methods and their impact on optimization results.
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MQL5 Trading Toolkit (Part 5): Expanding the History Management EX5 Library with Position Functions

MQL5 Trading Toolkit (Part 5): Expanding the History Management EX5 Library with Position Functions

Discover how to create exportable EX5 functions to efficiently query and save historical position data. In this step-by-step guide, we will expand the History Management EX5 library by developing modules that retrieve key properties of the most recently closed position. These include net profit, trade duration, pip-based stop loss, take profit, profit values, and various other important details.
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MQL5 Trading Tools (Part 16): Improved Super-Sampling Anti-Aliasing (SSAA) and High-Resolution Rendering

MQL5 Trading Tools (Part 16): Improved Super-Sampling Anti-Aliasing (SSAA) and High-Resolution Rendering

We add supersampling‑driven anti‑aliasing and high‑resolution rendering to the MQL5 canvas dashboard, then downsample to the target size. The article implements rounded rectangle fills and borders, rounded triangle arrows, and a custom scrollbar with theming for the stats and text panels. These tools help you build smoother, more legible UI components in MetaTrader 5.
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Market Simulation (Part 19): First Steps with SQL (II)

Market Simulation (Part 19): First Steps with SQL (II)

As we explained in the first article about SQL, there is no point in spending time programming procedures to do what is already built into SQL. However, without knowing the basics, you won’t be able to do anything with SQL or take full advantage of everything this tool offers. Therefore, in this article, we will look at how to perform basic tasks in databases.
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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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Two-sample Kolmogorov-Smirnov test as an indicator of time series non-stationarity

Two-sample Kolmogorov-Smirnov test as an indicator of time series non-stationarity

The article considers one of the most famous non-parametric homogeneity tests – the two-sample Kolmogorov-Smirnov test. Both model data and real quotes are analyzed. The article also provides an example of constructing a non-stationarity indicator (iSmirnovDistance).
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MQL5 Wizard Techniques you should know (Part 35): Support Vector Regression

MQL5 Wizard Techniques you should know (Part 35): Support Vector Regression

Support Vector Regression is an idealistic way of finding a function or ‘hyper-plane’ that best describes the relationship between two sets of data. We attempt to exploit this in time series forecasting within custom classes of the MQL5 wizard.
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Population optimization algorithms: Micro Artificial immune system (Micro-AIS)

Population optimization algorithms: Micro Artificial immune system (Micro-AIS)

The article considers an optimization method based on the principles of the body's immune system - Micro Artificial Immune System (Micro-AIS) - a modification of AIS. Micro-AIS uses a simpler model of the immune system and simple immune information processing operations. The article also discusses the advantages and disadvantages of Micro-AIS compared to conventional AIS.
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Market Simulation (Part 05): Creating the C_Orders Class (II)

Market Simulation (Part 05): Creating the C_Orders Class (II)

In this article, I will explain how Chart Trade, together with the Expert Advisor, will process a request to close all of the users' open positions. This may sound simple, but there are a few complications that you need to know how to manage.
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Gating mechanisms in ensemble learning

Gating mechanisms in ensemble learning

In this article, we continue our exploration of ensemble models by discussing the concept of gates, specifically how they may be useful in combining model outputs to enhance either prediction accuracy or model generalization.
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Example of Causality Network Analysis (CNA) and Vector Auto-Regression Model for Market Event Prediction

Example of Causality Network Analysis (CNA) and Vector Auto-Regression Model for Market Event Prediction

This article presents a comprehensive guide to implementing a sophisticated trading system using Causality Network Analysis (CNA) and Vector Autoregression (VAR) in MQL5. It covers the theoretical background of these methods, provides detailed explanations of key functions in the trading algorithm, and includes example code for implementation.
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Developing a Replay System (Part 64): Playing the service (V)

Developing a Replay System (Part 64): Playing the service (V)

In this article, we will look at how to fix two errors in the code. However, I will try to explain them in a way that will help you, beginner programmers, understand that things don't always go as you expect. Anyway, this is an opportunity to learn. The content presented here is intended solely for educational purposes. In no way should this application be considered as a final document with any purpose other than to explore the concepts presented.
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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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Analyzing binary code of prices on the exchange (Part I): A new look at technical analysis

Analyzing binary code of prices on the exchange (Part I): A new look at technical analysis

This article presents an innovative approach to technical analysis based on converting price movements into binary code. The author demonstrates how various aspects of market behavior — from simple price movements to complex patterns — can be encoded in a sequence of zeros and ones.
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Developing a Replay System (Part 30): Expert Advisor project — C_Mouse class (IV)

Developing a Replay System (Part 30): Expert Advisor project — C_Mouse class (IV)

Today we will learn a technique that can help us a lot in different stages of our professional life as a programmer. Often it is not the platform itself that is limited, but the knowledge of the person who talks about the limitations. This article will tell you that with common sense and creativity you can make the MetaTrader 5 platform much more interesting and versatile without resorting to creating crazy programs or anything like that, and create simple yet safe and reliable code. We will use our creativity to modify existing code without deleting or adding a single line to the source code.
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Eigenvectors and eigenvalues: Exploratory data analysis in MetaTrader 5

Eigenvectors and eigenvalues: Exploratory data analysis in MetaTrader 5

In this article we explore different ways in which the eigenvectors and eigenvalues can be applied in exploratory data analysis to reveal unique relationships in data.
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MQL5 Wizard Techniques you should know (Part 18): Neural Architecture Search with Eigen Vectors

MQL5 Wizard Techniques you should know (Part 18): Neural Architecture Search with Eigen Vectors

Neural Architecture Search, an automated approach at determining the ideal neural network settings can be a plus when facing many options and large test data sets. We examine how when paired Eigen Vectors this process can be made even more efficient.
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Hilbert-Schmidt Independence Criterion (HSIC)

Hilbert-Schmidt Independence Criterion (HSIC)

The article discusses the non-parametric HSIC (Hilbert-Schmidt Independence Criterion) statistical test designed to identify linear and non-linear dependencies in data. Implementations of two algorithms for calculating HSIC in the MQL5 language are proposed: the exact permutation test and the gamma approximation. The method efficiency is demonstrated on synthetic data modeling a non-linear relationship between features and the target variable.
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Markov Chain-Based Matrix Forecasting Model

Markov Chain-Based Matrix Forecasting Model

We are going to create a matrix forecasting model based on a Markov chain. What are Markov chains, and how can we use a Markov chain for Forex trading?
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Chaos optimization algorithm (COA): Continued

Chaos optimization algorithm (COA): Continued

We continue studying the chaotic optimization algorithm. The second part of the article deals with the practical aspects of the algorithm implementation, its testing and conclusions.
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Integrating MQL5 with Data Processing Packages (Part 8): Using Graph Neural Networks for Liquidity Zone Recognition

Integrating MQL5 with Data Processing Packages (Part 8): Using Graph Neural Networks for Liquidity Zone Recognition

This article shows how to represent market structure as a graph in MQL5, turning swing highs/lows into nodes with features and linking them by edges. It trains a Graph Neural Network to score potential liquidity zones, exports the model to ONNX, and runs real-time inference in an Expert Advisor. Readers learn how to build the data pipeline, integrate the model, visualize zones on the chart, and use the signals for rule-based execution.
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Market Simulation (Part 17): Sockets (XI)

Market Simulation (Part 17): Sockets (XI)

The implementation of the part of the code that will run in MetaTrader 5 does not present any difficulty. However, there are several points that need to be taken into account. This is necessary so that you can make the system work. Remember one important thing: not just one program will be running. In reality, we will have to run three programs simultaneously. It is important to implement and structure each of them in such a way that they can interact and communicate with one another, and that each of them understands what the others are trying or intending to do.
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The Group Method of Data Handling: Implementing the Multilayered Iterative Algorithm in MQL5

The Group Method of Data Handling: Implementing the Multilayered Iterative Algorithm in MQL5

In this article we describe the implementation of the Multilayered Iterative Algorithm of the Group Method of Data Handling in MQL5.
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Non-stationary processes and spurious regression

Non-stationary processes and spurious regression

The article demonstrates spurious regression occurring when attempting to apply regression analysis to non-stationary processes using Monte Carlo simulation.
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Integrating Computer Vision into Trading in MQL5 (Part 2): Extending the Architecture to 2D RGB Image Analysis

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.
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MQL5 Wizard Techniques you should know (Part 10). The Unconventional RBM

MQL5 Wizard Techniques you should know (Part 10). The Unconventional RBM

Restrictive Boltzmann Machines are at the basic level, a two-layer neural network that is proficient at unsupervised classification through dimensionality reduction. We take its basic principles and examine if we were to re-design and train it unorthodoxly, we could get a useful signal filter.
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Developing a Replay System (Part 57): Understanding a Test Service

Developing a Replay System (Part 57): Understanding a Test Service

One point to note: although the service code is not included in this article and will only be provided in the next one, I'll explain it since we'll be using that same code as a springboard for what we're actually developing. So, be attentive and patient. Wait for the next article, because every day everything becomes more interesting.