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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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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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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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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Creating Custom Indicators in MQL5 (Part 5): WaveTrend Crossover Evolution Using Canvas for Fog Gradients, Signal Bubbles, and Risk Management

Creating Custom Indicators in MQL5 (Part 5): WaveTrend Crossover Evolution Using Canvas for Fog Gradients, Signal Bubbles, and Risk Management

In this article, we enhance the Smart WaveTrend Crossover indicator in MQL5 by integrating canvas-based drawing for fog gradient overlays, signal boxes that detect breakouts, and customizable buy/sell bubbles or triangles for visual alerts. We incorporate risk management features with dynamic take-profit and stop-loss levels calculated via candle multipliers or percentages, displayed through lines and a table, alongside options for trend filtering and box extensions.
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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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From Novice to Expert: Market Periods Synchronizer

From Novice to Expert: Market Periods Synchronizer

In this discussion, we introduce a Higher-to-Lower Timeframe Synchronizer tool designed to solve the problem of analyzing market patterns that span across higher timeframe periods. The built-in period markers in MetaTrader 5 are often limited, rigid, and not easily customizable for non-standard timeframes. Our solution leverages the MQL5 language to develop an indicator that provides a dynamic and visual way to align higher timeframe structures within lower timeframe charts. This tool can be highly valuable for detailed market analysis. To learn more about its features and implementation, I invite you to join the discussion.
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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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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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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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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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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 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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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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MQL5 Trading Tools (Part 12): Enhancing the Correlation Matrix Dashboard with Interactivity

MQL5 Trading Tools (Part 12): Enhancing the Correlation Matrix Dashboard with Interactivity

In this article, we enhance the correlation matrix dashboard in MQL5 with interactive features like panel dragging, minimizing/maximizing, hover effects on buttons and timeframes, and mouse event handling for improved user experience. We add sorting of symbols by average correlation strength in ascending/descending modes, toggle between correlation and p-value views, and incorporate light/dark theme switching with dynamic color updates.
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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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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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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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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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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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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 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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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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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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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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Statistical Arbitrage Through Cointegrated Stocks (Part 9): Backtesting Portfolio Weights Updates

Statistical Arbitrage Through Cointegrated Stocks (Part 9): Backtesting Portfolio Weights Updates

This article describes the use of CSV files for backtesting portfolio weights updates in a mean-reversion-based strategy that uses statistical arbitrage through cointegrated stocks. It goes from feeding the database with the results of a Rolling Windows Eigenvector Comparison (RWEC) to comparing the backtest reports. In the meantime, the article details the role of each RWEC parameter and its impact in the overall backtest result, showing how the comparison of the relative drawdown can help us to further improve those parameters.
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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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Implementing Practical Modules from Other Languages in MQL5 (Part 04): time, date, and datetime modules from Python

Implementing Practical Modules from Other Languages in MQL5 (Part 04): time, date, and datetime modules from Python

Unlike MQL5, Python programming language offers control and flexibility when it comes to dealing with and manipulating time. In this article, we will implement similar modules for better handling of dates and time in MQL5 as in Python.
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Integrating MQL5 with Data Processing Packages (Part 6): Merging Market Feedback with Model Adaptation

Integrating MQL5 with Data Processing Packages (Part 6): Merging Market Feedback with Model Adaptation

In this part, we focus on how to merge real-time market feedback—such as live trade outcomes, volatility changes, and liquidity shifts—with adaptive model learning to maintain a responsive and self-improving trading system.
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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 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.
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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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Developing a Replay System (Part 60): Playing the Service (I)

Developing a Replay System (Part 60): Playing the Service (I)

We have been working on just the indicators for a long time now, but now it's time to get the service working again and see how the chart is built based on the data provided. However, since the whole thing is not that simple, we will have to be attentive to understand what awaits us ahead.
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A feature selection algorithm using energy based learning in pure MQL5

A feature selection algorithm using energy based learning in pure MQL5

In this article we present the implementation of a feature selection algorithm described in an academic paper titled,"FREL: A stable feature selection algorithm", called Feature weighting as regularized energy based learning.
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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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MQL5 Trading Toolkit (Part 6): Expanding the History Management EX5 Library with the Last Filled Pending Order Functions

MQL5 Trading Toolkit (Part 6): Expanding the History Management EX5 Library with the Last Filled Pending Order Functions

Learn how to create an EX5 module of exportable functions that seamlessly query and save data for the most recently filled pending order. In this comprehensive step-by-step guide, we will enhance the History Management EX5 library by developing dedicated and compartmentalized functions to retrieve essential properties of the last filled pending order. These properties include the order type, setup time, execution time, filling type, and other critical details necessary for effective pending orders trade history management and analysis.
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Atmosphere Clouds Model Optimization (ACMO): Theory

Atmosphere Clouds Model Optimization (ACMO): Theory

The article is devoted to the metaheuristic Atmosphere Clouds Model Optimization (ACMO) algorithm, which simulates the behavior of clouds to solve optimization problems. The algorithm uses the principles of cloud generation, movement and propagation, adapting to the "weather conditions" in the solution space. The article reveals how the algorithm's meteorological simulation finds optimal solutions in a complex possibility space and describes in detail the stages of ACMO operation, including "sky" preparation, cloud birth, cloud movement, and rain concentration.
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Adaptive Social Behavior Optimization (ASBO): Two-phase evolution

Adaptive Social Behavior Optimization (ASBO): Two-phase evolution

We continue dwelling on the topic of social behavior of living organisms and its impact on the development of a new mathematical model - ASBO (Adaptive Social Behavior Optimization). We will dive into the two-phase evolution, test the algorithm and draw conclusions. Just as in nature a group of living organisms join their efforts to survive, ASBO uses principles of collective behavior to solve complex optimization problems.
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The case for using Hospital-Performance Data with Perceptrons, this Q4, in weighing SPDR XLV's next Performance

The case for using Hospital-Performance Data with Perceptrons, this Q4, in weighing SPDR XLV's next Performance

XLV is SPDR healthcare ETF and in an age where it is common to be bombarded by a wide array of traditional news items plus social media feeds, it can be pressing to select a data set for use with a model. We try to tackle this problem for this ETF by sizing up some of its critical data sets in MQL5.
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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 45): Chart Trade Project (IV)

Developing a Replay System (Part 45): Chart Trade Project (IV)

The main purpose of this article is to introduce and explain the C_ChartFloatingRAD class. We have a Chart Trade indicator that works in a rather interesting way. As you may have noticed, we still have a fairly small number of objects on the chart, and yet we get the expected functionality. The values present in the indicator can be edited. The question is, how is this possible? This article will start to make things clearer.