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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Deterministic Oscillatory Search (DOS)

Deterministic Oscillatory Search (DOS)

Deterministic Oscillatory Search (DOS) algorithm is an innovative global optimization method that combines the advantages of gradient and swarm algorithms without the use of random numbers. The fitness oscillation and slope mechanism allows DOS to explore complex search spaces in a deterministic manner.
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Automatic Session Volume Profile Builder in MQL5: Rendering POC and Value Area Without Third-Party Tools

Automatic Session Volume Profile Builder in MQL5: Rendering POC and Value Area Without Third-Party Tools

Implement a session-focused volume profile in MQL5: acquire ticks with CopyTicksRange(), bin prices, and compute POC, VAH, and VAL by the 70% approach. The indicator renders directly on the chart as native objects, supports fixed-width scaling for consistent geometry across timeframes, and refreshes on each new session. This provides objective reference levels without external dependencies.
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Market Simulation (Part 02): Cross Orders (II)

Market Simulation (Part 02): Cross Orders (II)

Unlike what was done in the previous article, here we will test the selection option using an Expert Advisor. Although this is not a final solution yet, it will be enough for now. With the help of this article, you will be able to understand how to implement one of the possible solutions.
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Hybridization of population algorithms. Sequential and parallel structures

Hybridization of population algorithms. Sequential and parallel structures

Here we will dive into the world of hybridization of optimization algorithms by looking at three key types: strategy mixing, sequential and parallel hybridization. We will conduct a series of experiments combining and testing relevant optimization algorithms.
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Developing a Replay System (Part 33): Order System (II)

Developing a Replay System (Part 33): Order System (II)

Today we will continue to develop the order system. As you will see, we will be massively reusing what has already been shown in other articles. Nevertheless, you will receive a small reward in this article. First, we will develop a system that can be used with a real trading server, both from a demo account or from a real one. We will make extensive use of the MetaTrader 5 platform, which will provide us with all the necessary support from the beginning.
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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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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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Application of the Grey Model in Technical Analysis of Financial Time Series

Application of the Grey Model in Technical Analysis of Financial Time Series

This article explores the grey model, a promising tool that can expand trader's capabilities. We will look at some options for applying this model to technical analysis and building trading strategies.
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Ordinal Encoding for Nominal Variables

Ordinal Encoding for Nominal Variables

In this article, we discuss and demonstrate how to convert nominal predictors into numerical formats that are suitable for machine learning algorithms, using both Python and MQL5.
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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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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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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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Ensemble methods to enhance classification tasks in MQL5

Ensemble methods to enhance classification tasks in MQL5

In this article, we present the implementation of several ensemble classifiers in MQL5 and discuss their efficacy in varying situations.
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Applying Localized Feature Selection in Python and MQL5

Applying Localized Feature Selection in Python and MQL5

This article explores a feature selection algorithm introduced in the paper 'Local Feature Selection for Data Classification' by Narges Armanfard et al. The algorithm is implemented in Python to build binary classifier models that can be integrated with MetaTrader 5 applications for inference.
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Category Theory in MQL5 (Part 12): Orders

Category Theory in MQL5 (Part 12): Orders

This article which is part of a series that follows Category Theory implementation of Graphs in MQL5, delves in Orders. We examine how concepts of Order-Theory can support monoid sets in informing trade decisions by considering two major ordering types.
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Artificial Tribe Algorithm (ATA)

Artificial Tribe Algorithm (ATA)

The article provides a detailed discussion of the key components and innovations of the ATA optimization algorithm, which is an evolutionary method with a unique dual behavior system that adapts depending on the situation. ATA combines individual and social learning while using crossover for explorations and migration to find solutions when stuck in local optima.
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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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Developing a Replay System (Part 68): Getting the Time Right (I)

Developing a Replay System (Part 68): Getting the Time Right (I)

Today we will continue working on getting the mouse pointer to tell us how much time is left on a bar during periods of low liquidity. Although at first glance it seems simple, in reality this task is much more difficult. This involves some obstacles that we will have to overcome. Therefore, it is important that you have a good understanding of the material in this first part of this subseries in order to understand the following parts.
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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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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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Extremal Optimization (EO)

Extremal Optimization (EO)

The article discusses the Extremal Optimization (EO) algorithm, an optimization method inspired by the Bak-Sneppen self-organized criticality model, where evolution occurs through the elimination of the worst-case components of the system. The modified population version of the algorithm demonstrates a shift away from theoretical principles in favor of practical efficiency, leading to the creation of powerful computational tools.
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Analyzing weather impact on currencies of agricultural countries using Python

Analyzing weather impact on currencies of agricultural countries using Python

What is the relationship between weather and Forex? Classical economic theory has long ignored the influence of such factors as weather on market behavior. But everything has changed. Let's try to find connections between the weather conditions and the position of agricultural currencies on the market.
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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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MQL5 Wizard Techniques you should know (Part 54): Reinforcement Learning with hybrid SAC and Tensors

MQL5 Wizard Techniques you should know (Part 54): Reinforcement Learning with hybrid SAC and Tensors

Soft Actor Critic is a Reinforcement Learning algorithm that we looked at in a previous article, where we also introduced python and ONNX to these series as efficient approaches to training networks. We revisit the algorithm with the aim of exploiting tensors, computational graphs that are often exploited in Python.
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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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A Team of AI Agents with Profit-Based Rotation: The Evolution of a Living Trading System in MQL5

A Team of AI Agents with Profit-Based Rotation: The Evolution of a Living Trading System in MQL5

Financial management as an ecosystem: Seven AI traders with different personalities and strategies instead of a single algorithm. They compete for capital, learn from their mistakes, and make decisions collectively. The article explains the principles behind the Modern RL Trader system, in which the code possesses consciousness and emotions, creating a living, evolving trading mind.
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MQL5 Wizard Techniques you should know (Part 47): Reinforcement Learning with Temporal Difference

MQL5 Wizard Techniques you should know (Part 47): Reinforcement Learning with Temporal Difference

Temporal Difference is another algorithm in reinforcement learning that updates Q-Values basing on the difference between predicted and actual rewards during agent training. It specifically dwells on updating Q-Values without minding their state-action pairing. We therefore look to see how to apply this, as we have with previous articles, in a wizard assembled Expert Advisor.
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Role of random number generator quality in the efficiency of optimization algorithms

Role of random number generator quality in the efficiency of optimization algorithms

In this article, we will look at the Mersenne Twister random number generator and compare it with the standard one in MQL5. We will also find out the influence of the random number generator quality on the results of optimization algorithms.
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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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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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Fast Integration of a Large Language Model with MetaTrader 5 (Part II): Fine-Tuning on Real Data, Backtesting, and Live Trading by the Model

Fast Integration of a Large Language Model with MetaTrader 5 (Part II): Fine-Tuning on Real Data, Backtesting, and Live Trading by the Model

The article describes the process of fine-tuning a language model for trading based on real historical data from MetaTrader 5. The base model, which has only theoretical knowledge of technical analysis, is trained on a thousand examples of the real behavior of currency pairs (EURUSD, GBPUSD, USDCHF, USDCAD) over 180 days. After being trained using Ollama, the model begins to understand the specific characteristics of each instrument.
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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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Linear Regression Prediction Channels in MQL5: Constructing Statistically Grounded Confidence and Prediction Bands

Linear Regression Prediction Channels in MQL5: Constructing Statistically Grounded Confidence and Prediction Bands

The article implements rolling OLS regression channels in MQL5 and computes confidence and prediction bands with Student's t critical values instead of a fixed standard-deviation multiplier. It explains the leverage-driven widening at window edges, contrasts the result with Bollinger and Donchian channels, and reviews OLS assumptions on price data. A five-line rendering is documented to ensure reliable display in MetaTrader 5.
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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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Price Action Analysis Toolkit Development (Part 76): One-Click Symbol Dashboard for Centralized Multi-Chart Management in MQL5

Price Action Analysis Toolkit Development (Part 76): One-Click Symbol Dashboard for Centralized Multi-Chart Management in MQL5

Learn to assemble an MT5 Expert Advisor that hosts a chart management dashboard written in MQL5. The guide walks through shared definitions, symbol acquisition and filtering, chart lifecycle functions, and a UI panel with search, scrolling, and state indicators, all driven by events and a timer. The result is a reproducible tool that reduces clicks and accelerates multi-symbol analysis.
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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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Feature Engineering for ML (Part 2): Implementing Fixed-Width Fractional Differentiation in MQL5

Feature Engineering for ML (Part 2): Implementing Fixed-Width Fractional Differentiation in MQL5

This article delivers a production-grade MQL5 implementation of fixed-width fractional differentiation for live MetaTrader 5 feeds. We introduce a header-only CFFDEngine that precomputes weights without a fixed cap, performs O(width) per-bar updates, and avoids per-tick allocations. The FFD.mq5 indicator supports all ENUM_APPLIED_PRICE types and prev_calculated optimization. Validation scripts confirm numerical equivalence with the standard Python frac diff_ffd pipeline.
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MQL5 Wizard Techniques you should know (14): Multi Objective Timeseries Forecasting with STF

MQL5 Wizard Techniques you should know (14): Multi Objective Timeseries Forecasting with STF

Spatial Temporal Fusion which is using both ‘space’ and time metrics in modelling data is primarily useful in remote-sensing, and a host of other visual based activities in gaining a better understanding of our surroundings. Thanks to a published paper, we take a novel approach in using it by examining its potential to traders.
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Population optimization algorithms: Evolution of Social Groups (ESG)

Population optimization algorithms: Evolution of Social Groups (ESG)

We will consider the principle of constructing multi-population algorithms. As an example of this type of algorithm, we will have a look at the new custom algorithm - Evolution of Social Groups (ESG). We will analyze the basic concepts, population interaction mechanisms and advantages of this algorithm, as well as examine its performance in optimization problems.
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Building a Correlation-Aware Portfolio Risk Monitor in MQL5

Building a Correlation-Aware Portfolio Risk Monitor in MQL5

The article quantifies correlation and portfolio risk in MetaTrader 5: from time-aligned returns to a covariance matrix, true portfolio variance against the independent-sum assumption, and position-level risk attribution. A MetaTrader 5 service runs in the background, shows the metrics on a small chart panel, and pushes alerts when risk thresholds are crossed. Source code is provided for an example script, a reusable risk engine class, and the service.