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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Selection and navigation utility in MQL5 and MQL4: Adding auto search for patterns and displaying detected symbols
Selection and navigation utility in MQL5 and MQL4: Adding auto search for patterns and displaying detected symbols

Selection and navigation utility in MQL5 and MQL4: Adding auto search for patterns and displaying detected symbols

In this article, we continue expanding the features of the utility for collecting and navigating through symbols. This time, we will create new tabs displaying only the symbols that satisfy some of the necessary parameters and find out how to easily add custom tabs with the necessary sorting rules.
Naive Bayes classifier for signals of a set of indicators
Naive Bayes classifier for signals of a set of indicators

Naive Bayes classifier for signals of a set of indicators

The article analyzes the application of the Bayes' formula for increasing the reliability of trading systems by means of using signals from multiple independent indicators. Theoretical calculations are verified with a simple universal EA, configured to work with arbitrary indicators.
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Python + MetaTrader 5: Fast Research Framework for Data, Features, and Prototypes

Python + MetaTrader 5: Fast Research Framework for Data, Features, and Prototypes

The article demonstrates how Python and MetaTrader 5 integration combines research flexibility and trade execution into a single workflow. Python is used for data analysis, feature selection and model training, while MetaTrader 5 is used for testing and trading automation. This approach simplifies the transfer of solutions into practice, increases reproducibility, and makes the development of trading systems faster and more structured.
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Data Science and Machine Learning — Neural Network (Part 02): Feed forward NN Architectures Design

Data Science and Machine Learning — Neural Network (Part 02): Feed forward NN Architectures Design

There are minor things to cover on the feed-forward neural network before we are through, the design being one of them. Let's see how we can build and design a flexible neural network to our inputs, the number of hidden layers, and the nodes for each of the network.
Library for easy and quick development of MetaTrader programs (part XVI): Symbol collection events
Library for easy and quick development of MetaTrader programs (part XVI): Symbol collection events

Library for easy and quick development of MetaTrader programs (part XVI): Symbol collection events

In this article, we will create a new base class of all library objects adding the event functionality to all its descendants and develop the class for tracking symbol collection events based on the new base class. We will also change account and account event classes for developing the new base object functionality.
Universal Regression Model for Market Price Prediction
Universal Regression Model for Market Price Prediction

Universal Regression Model for Market Price Prediction

The market price is formed out of a stable balance between demand and supply which, in turn, depend on a variety of economic, political and psychological factors. Differences in nature as well as causes of influence of these factors make it difficult to directly consider all the components. This article sets forth an attempt to predict the market price on the basis of an elaborated regression model.
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Price Action Analysis Toolkit Development (Part 44): Building a VWMA Crossover Signal EA in MQL5

Price Action Analysis Toolkit Development (Part 44): Building a VWMA Crossover Signal EA in MQL5

This article introduces a VWMA crossover signal tool for MetaTrader 5, designed to help traders identify potential bullish and bearish reversals by combining price action with trading volume. The EA generates clear buy and sell signals directly on the chart, features an informative panel, and allows for full user customization, making it a practical addition to your trading strategy.
Social Trading. Can a profitable signal be made even better?
Social Trading. Can a profitable signal be made even better?

Social Trading. Can a profitable signal be made even better?

Most subscribers choose a trade signal by the beauty of the balance curve and by the number of subscribers. This is why many today's providers care of beautiful statistics rather than of real signal quality, often playing with lot sizes and artificially reducing the balance curve to an ideal appearance. This paper deals with the reliability criteria and the methods a provider may use to enhance its signal quality. An exemplary analysis of a specific signal history is presented, as well as methods that would help a provider to make it more profitable and less risky.
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Price Action Analysis Toolkit Development (Part 27): Liquidity Sweep With MA Filter Tool

Price Action Analysis Toolkit Development (Part 27): Liquidity Sweep With MA Filter Tool

Understanding the subtle dynamics behind price movements can give you a critical edge. One such phenomenon is the liquidity sweep, a deliberate strategy that large traders, especially institutions, use to push prices through key support or resistance levels. These levels often coincide with clusters of retail stop-loss orders, creating pockets of liquidity that big players can exploit to enter or exit sizeable positions with minimal slippage.
Statistical Carry Trade Strategy
Statistical Carry Trade Strategy

Statistical Carry Trade Strategy

An algorithm of statistical protection of open positive swap positions from unwanted price movements. This article features a variant of the carry trade protection strategy that allows to compensate for potential risk of the price movement in the direction opposite to that of the open position.
Library for easy and quick development of MetaTrader programs (part XII): Account object class and collection of account objects
Library for easy and quick development of MetaTrader programs (part XII): Account object class and collection of account objects

Library for easy and quick development of MetaTrader programs (part XII): Account object class and collection of account objects

In the previous article, we defined position closure events for MQL4 in the library and got rid of the unused order properties. Here we will consider the creation of the Account object, develop the collection of account objects and prepare the functionality for tracking account events.
Visualizing trading strategy optimization in MetaTrader 5
Visualizing trading strategy optimization in MetaTrader 5

Visualizing trading strategy optimization in MetaTrader 5

The article implements an MQL application with a graphical interface for extended visualization of the optimization process. The graphical interface applies the last version of EasyAndFast library. Many users may ask why they need graphical interfaces in MQL applications. This article demonstrates one of multiple cases where they can be useful for traders.
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Neural networks made easy (Part 8): Attention mechanisms

Neural networks made easy (Part 8): Attention mechanisms

In previous articles, we have already tested various options for organizing neural networks. We also considered convolutional networks borrowed from image processing algorithms. In this article, I suggest considering Attention Mechanisms, the appearance of which gave impetus to the development of language models.
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Price Action Analysis Toolkit Development (Part 53): Pattern Density Heatmap for Support and Resistance Zone Discovery

Price Action Analysis Toolkit Development (Part 53): Pattern Density Heatmap for Support and Resistance Zone Discovery

This article introduces the Pattern Density Heatmap, a price‑action mapping tool that transforms repeated candlestick pattern detections into statistically significant support and resistance zones. Rather than treating each signal in isolation, the EA aggregates detections into fixed price bins, scores their density with optional recency weighting, and confirms levels against higher‑timeframe data. The resulting heatmap reveals where the market has historically reacted—levels that can be used proactively for trade timing, risk management, and strategy confidence across any trading style.
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Mastering Fair Value Gaps: Formation, Logic, and Automated Trading with Breakers and Market Structure Shifts

Mastering Fair Value Gaps: Formation, Logic, and Automated Trading with Breakers and Market Structure Shifts

This is an article that I have written aimed to expound and explain Fair Value Gaps, their formation logic for occurring, and automated trading with breakers and market structure shifts.
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Mastering ONNX: The Game-Changer for MQL5 Traders

Mastering ONNX: The Game-Changer for MQL5 Traders

Dive into the world of ONNX, the powerful open-standard format for exchanging machine learning models. Discover how leveraging ONNX can revolutionize algorithmic trading in MQL5, allowing traders to seamlessly integrate cutting-edge AI models and elevate their strategies to new heights. Uncover the secrets to cross-platform compatibility and learn how to unlock the full potential of ONNX in your MQL5 trading endeavors. Elevate your trading game with this comprehensive guide to Mastering ONNX
Applying OLAP in trading (part 2): Visualizing the interactive multidimensional data analysis results
Applying OLAP in trading (part 2): Visualizing the interactive multidimensional data analysis results

Applying OLAP in trading (part 2): Visualizing the interactive multidimensional data analysis results

In this article, we consider the creation of an interactive graphical interface for an MQL program, which is designed for the processing of account history and trading reports using OLAP techniques. To obtain a visual result, we will use maximizable and scalable windows, an adaptive layout of rubber controls and a new control for displaying diagrams. To provide the visualization functionality, we will implement a GUI with the selection of variables along coordinate axes, as well as with the selection of aggregate functions, diagram types and sorting options.
Risk Evaluation in the Sequence of Deals with One Asset
Risk Evaluation in the Sequence of Deals with One Asset

Risk Evaluation in the Sequence of Deals with One Asset

This article describes the use of methods of the theory of probability and mathematical statistics in the analysis of trading systems.
Combinatorics and probability theory for trading (Part III): The first mathematical model
Combinatorics and probability theory for trading (Part III): The first mathematical model

Combinatorics and probability theory for trading (Part III): The first mathematical model

A logical continuation of the earlier discussed topic would be the development of multifunctional mathematical models for trading tasks. In this article, I will describe the entire process related to the development of the first mathematical model describing fractals, from scratch. This model should become an important building block and be multifunctional and universal. It will build up our theoretical basis for further development of this idea.
The market and the physics of its global patterns
The market and the physics of its global patterns

The market and the physics of its global patterns

In this article, I will try to test the assumption that any system with even a small understanding of the market can operate on a global scale. I will not invent any theories or patterns, but I will only use known facts, gradually translating these facts into the language of mathematical analysis.
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Trader-friendly stop loss and take profit

Trader-friendly stop loss and take profit

Stop loss and take profit can have a significant impact on trading results. In this article, we will look at several ways to find optimal stop order values.
Library for easy and quick development of MetaTrader programs (part X): Compatibility with MQL4 - Events of opening a position and activating pending orders
Library for easy and quick development of MetaTrader programs (part X): Compatibility with MQL4 - Events of opening a position and activating pending orders

Library for easy and quick development of MetaTrader programs (part X): Compatibility with MQL4 - Events of opening a position and activating pending orders

In the previous articles, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. In the ninth part, we started improving the library classes for working with MQL4. Here we will continue improving the library to ensure its full compatibility with MQL4.
Library for easy and quick development of MetaTrader programs (part VIII): Order and position modification events
Library for easy and quick development of MetaTrader programs (part VIII): Order and position modification events

Library for easy and quick development of MetaTrader programs (part VIII): Order and position modification events

In the previous articles, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. In the seventh part, we added tracking StopLimit orders activation and prepared the functionality for tracking other events involving orders and positions. In this article, we will develop the class for tracking order and position modification events.
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Data Science and Machine Learning (Part 03): Matrix Regressions

Data Science and Machine Learning (Part 03): Matrix Regressions

This time our models are being made by matrices, which allows flexibility while it allows us to make powerful models that can handle not only five independent variables but also many variables as long as we stay within the calculations limits of a computer, this article is going to be an interesting read, that's for sure.
Separate optimization of a strategy on trend and flat conditions
Separate optimization of a strategy on trend and flat conditions

Separate optimization of a strategy on trend and flat conditions

The article considers applying the separate optimization method during various market conditions. Separate optimization means defining trading system's optimal parameters by optimizing for an uptrend and downtrend separately. To reduce the effect of false signals and improve profitability, the systems are made flexible, meaning they have some specific set of settings or input data, which is justified because the market behavior is constantly changing.
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Neural networks made easy (Part 3): Convolutional networks

Neural networks made easy (Part 3): Convolutional networks

As a continuation of the neural network topic, I propose considering convolutional neural networks. This type of neural network are usually applied to analyzing visual imagery. In this article, we will consider the application of these networks in the financial markets.
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Brute force approach to pattern search

Brute force approach to pattern search

In this article, we will search for market patterns, create Expert Advisors based on the identified patterns, and check how long these patterns remain valid, if they ever retain their validity.
Information Storage and View
Information Storage and View

Information Storage and View

The article deals with convenient and efficient methods of information storage and viewing. Alternatives to the terminal standard log file and the Comment() function are considered here.
Combinatorics and probability theory for trading (Part II): Universal fractal
Combinatorics and probability theory for trading (Part II): Universal fractal

Combinatorics and probability theory for trading (Part II): Universal fractal

In this article, we will continue to study fractals and will pay special attention to summarizing all the material. To do this, I will try to bring all earlier developments into a compact form which would be convenient and understandable for practical application in trading.
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Neural networks made easy (Part 9): Documenting the work

Neural networks made easy (Part 9): Documenting the work

We have already passed a long way and the code in our library is becoming bigger and bigger. This makes it difficult to keep track of all connections and dependencies. Therefore, I suggest creating documentation for the earlier created code and to keep it updating with each new step. Properly prepared documentation will help us see the integrity of our work.
Econometric Approach to Analysis of Charts
Econometric Approach to Analysis of Charts

Econometric Approach to Analysis of Charts

This article describes the econometric methods of analysis, the autocorrelation analysis and the analysis of conditional variance in particular. What is the benefit of the approach described here? Use of the non-linear GARCH models allows representing the analyzed series formally from the mathematical point of view and creating a forecast for a specified number of steps.
Combinatorics and probability for trading (Part IV): Bernoulli Logic
Combinatorics and probability for trading (Part IV): Bernoulli Logic

Combinatorics and probability for trading (Part IV): Bernoulli Logic

In this article, I decided to highlight the well-known Bernoulli scheme and to show how it can be used to describe trading-related data arrays. All this will then be used to create a self-adapting trading system. We will also look for a more generic algorithm, a special case of which is the Bernoulli formula, and will find an application for it.
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Price Action Analysis Toolkit Development (Part 32): Python Candlestick Recognition Engine (II) — Detection Using Ta-Lib

Price Action Analysis Toolkit Development (Part 32): Python Candlestick Recognition Engine (II) — Detection Using Ta-Lib

In this article, we’ve transitioned from manually coding candlestick‑pattern detection in Python to leveraging TA‑Lib, a library that recognizes over sixty distinct patterns. These formations offer valuable insights into potential market reversals and trend continuations. Follow along to learn more.
How to visualize multicurrency trading history based on HTML and CSV reports
How to visualize multicurrency trading history based on HTML and CSV reports

How to visualize multicurrency trading history based on HTML and CSV reports

Since its introduction, MetaTrader 5 provides multicurrency testing options. This possibility is often used by traders. However the function is not universal. The article presents several programs for drawing graphical objects on charts based on HTML and CSV trading history reports. Multicurrency trading can be analyzed in parallel, in several sub-windows, as well as in one window using the dynamic switching command.
Other classes in DoEasy library (Part 66): MQL5.com Signals collection class
Other classes in DoEasy library (Part 66): MQL5.com Signals collection class

Other classes in DoEasy library (Part 66): MQL5.com Signals collection class

In this article, I will create the signal collection class of the MQL5.com Signals service with the functions for managing signals. Besides, I will improve the Depth of Market snapshot object class for displaying the total DOM buy and sell volumes.
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Matrix and Vector operations in MQL5

Matrix and Vector operations in MQL5

Matrices and vectors have been introduced in MQL5 for efficient operations with mathematical solutions. The new types offer built-in methods for creating concise and understandable code that is close to mathematical notation. Arrays provide extensive capabilities, but there are many cases in which matrices are much more efficient.
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Neural networks made easy (Part 5): Multithreaded calculations in OpenCL

Neural networks made easy (Part 5): Multithreaded calculations in OpenCL

We have earlier discussed some types of neural network implementations. In the considered networks, the same operations are repeated for each neuron. A logical further step is to utilize multithreaded computing capabilities provided by modern technology in an effort to speed up the neural network learning process. One of the possible implementations is described in this article.
Controlling the Slope of Balance Curve During Work of an Expert Advisor
Controlling the Slope of Balance Curve During Work of an Expert Advisor

Controlling the Slope of Balance Curve During Work of an Expert Advisor

Finding rules for a trade system and programming them in an Expert Advisor is a half of the job. Somehow, you need to correct the operation of the Expert Advisor as it accumulates the results of trading. This article describes one of approaches, which allows improving performance of an Expert Advisor through creation of a feedback that measures slope of the balance curve.
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MetaTrader 5 Machine Learning Blueprint (Part 2): Labeling Financial Data for Machine Learning

MetaTrader 5 Machine Learning Blueprint (Part 2): Labeling Financial Data for Machine Learning

In this second installment of the MetaTrader 5 Machine Learning Blueprint series, you’ll discover why simple labels can lead your models astray—and how to apply advanced techniques like the Triple-Barrier and Trend-Scanning methods to define robust, risk-aware targets. Packed with practical Python examples that optimize these computationally intensive techniques, this hands-on guide shows you how to transform noisy market data into reliable labels that mirror real-world trading conditions.
Library for easy and quick development of MetaTrader programs (part III). Collection of market orders and positions, search and sorting
Library for easy and quick development of MetaTrader programs (part III). Collection of market orders and positions, search and sorting

Library for easy and quick development of MetaTrader programs (part III). Collection of market orders and positions, search and sorting

In the first part, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. Further on, we implemented the collection of history orders and deals. Our next step is creating a class for a convenient selection and sorting of orders, deals and positions in collection lists. We are going to implement the base library object called Engine and add collection of market orders and positions to the library.