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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Big Bang - Big Crunch (BBBC) algorithm

Big Bang - Big Crunch (BBBC) algorithm

The article presents the Big Bang - Big Crunch method, which has two key phases: cyclic generation of random points and their compression to the optimal solution. This approach combines exploration and refinement, allowing us to gradually find better solutions and open up new optimization opportunities.
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The base class of population algorithms as the backbone of efficient optimization

The base class of population algorithms as the backbone of efficient optimization

The article represents a unique research attempt to combine a variety of population algorithms into a single class to simplify the application of optimization methods. This approach not only opens up opportunities for the development of new algorithms, including hybrid variants, but also creates a universal basic test stand. This stand becomes a key tool for choosing the optimal algorithm depending on a specific task.
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Price Action Analysis Toolkit Development (Part 18): Introducing Quarters Theory (III) — Quarters Board

Price Action Analysis Toolkit Development (Part 18): Introducing Quarters Theory (III) — Quarters Board

In this article, we enhance the original Quarters Script by introducing the Quarters Board, a tool that lets you toggle quarter levels directly on the chart without needing to revisit the code. You can easily activate or deactivate specific levels, and the EA also provides trend direction commentary to help you better understand market movements.
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Data Science and ML (Part 39): News + Artificial Intelligence, Would You Bet on it?

Data Science and ML (Part 39): News + Artificial Intelligence, Would You Bet on it?

News drives the financial markets, especially major releases like Non-Farm Payrolls (NFPs). We've all witnessed how a single headline can trigger sharp price movements. In this article, we dive into the powerful intersection of news data and Artificial Intelligence.
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From Novice to Expert: Animated News Headline Using MQL5 (I)

From Novice to Expert: Animated News Headline Using MQL5 (I)

News accessibility is a critical factor when trading on the MetaTrader 5 terminal. While numerous news APIs are available, many traders face challenges in accessing and integrating them effectively into their trading environment. In this discussion, we aim to develop a streamlined solution that brings news directly onto the chart—where it’s most needed. We'll accomplish this by building a News Headline Expert Advisor that monitors and displays real-time news updates from API sources.
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Developing a Replay System (Part 31): Expert Advisor project — C_Mouse class (V)

Developing a Replay System (Part 31): Expert Advisor project — C_Mouse class (V)

We need a timer that can show how much time is left till the end of the replay/simulation run. This may seem at first glance to be a simple and quick solution. Many simply try to adapt and use the same system that the trading server uses. But there's one thing that many people don't consider when thinking about this solution: with replay, and even m ore with simulation, the clock works differently. All this complicates the creation of such a system.
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Feature Engineering With Python And MQL5 (Part II): Angle Of Price

Feature Engineering With Python And MQL5 (Part II): Angle Of Price

There are many posts in the MQL5 Forum asking for help calculating the slope of price changes. This article will demonstrate one possible way of calculating the angle formed by the changes in price in any market you wish to trade. Additionally, we will answer if engineering this new feature is worth the extra effort and time invested. We will explore if the slope of the price can improve any of our AI model's accuracy when forecasting the USDZAR pair on the M1.
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Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (I)

Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (I)

This discussion delves into the challenges encountered when working with large codebases. We will explore the best practices for code organization in MQL5 and implement a practical approach to enhance the readability and scalability of our Trading Administrator Panel source code. Additionally, we aim to develop reusable code components that can potentially benefit other developers in their algorithm development. Read on and join the conversation.
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Developing a Replay System (Part 44): Chart Trade Project (III)

Developing a Replay System (Part 44): Chart Trade Project (III)

In the previous article I explained how you can manipulate template data for use in OBJ_CHART. In that article, I only outlined the topic without going into details, since in that version the work was done in a very simplified way. This was done to make it easier to explain the content, because despite the apparent simplicity of many things, some of them were not so obvious, and without understanding the simplest and most basic part, you would not be able to truly understand the entire picture.
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Chemical reaction optimization (CRO) algorithm (Part II): Assembling and results

Chemical reaction optimization (CRO) algorithm (Part II): Assembling and results

In the second part, we will collect chemical operators into a single algorithm and present a detailed analysis of its results. Let's find out how the Chemical reaction optimization (CRO) method copes with solving complex problems on test functions.
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Price Action Analysis Toolkit Development (Part 9): External Flow

Price Action Analysis Toolkit Development (Part 9): External Flow

This article explores a new dimension of analysis using external libraries specifically designed for advanced analytics. These libraries, like pandas, provide powerful tools for processing and interpreting complex data, enabling traders to gain more profound insights into market dynamics. By integrating such technologies, we can bridge the gap between raw data and actionable strategies. Join us as we lay the foundation for this innovative approach and unlock the potential of combining technology with trading expertise.
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Category Theory in MQL5 (Part 6): Monomorphic Pull-Backs and Epimorphic Push-Outs

Category Theory in MQL5 (Part 6): Monomorphic Pull-Backs and Epimorphic Push-Outs

Category Theory is a diverse and expanding branch of Mathematics which is only recently getting some coverage in the MQL5 community. These series of articles look to explore and examine some of its concepts & axioms with the overall goal of establishing an open library that provides insight while also hopefully furthering the use of this remarkable field in Traders' strategy development.
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Developing a Replay System (Part 66): Playing the service (VII)

Developing a Replay System (Part 66): Playing the service (VII)

In this article, we will implement the first solution that will allow us to determine when a new bar may appear on the chart. This solution is applicable in a wide variety of situations. Understanding its development will help you grasp several important aspects. 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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Combinatorially Symmetric Cross Validation In MQL5

Combinatorially Symmetric Cross Validation In MQL5

In this article we present the implementation of Combinatorially Symmetric Cross Validation in pure MQL5, to measure the degree to which a overfitting may occure after optimizing a strategy using the slow complete algorithm of the Strategy Tester.
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Developing a Replay System (Part 49): Things Get Complicated (I)

Developing a Replay System (Part 49): Things Get Complicated (I)

In this article, we'll complicate things a little. Using what was shown in the previous articles, we will start to open up the template file so that the user can use their own template. However, I will be making changes gradually, as I will also be refining the indicator to reduce the load on MetaTrader 5.
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Royal Flush Optimization (RFO)

Royal Flush Optimization (RFO)

The original Royal Flush Optimization algorithm offers a new approach to solving optimization problems, replacing the classic binary coding of genetic algorithms with a sector-based approach inspired by poker principles. RFO demonstrates how simplifying basic principles can lead to an efficient and practical optimization method. The article presents a detailed analysis of the algorithm and test results.
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Artificial Ecosystem-based Optimization (AEO) algorithm

Artificial Ecosystem-based Optimization (AEO) algorithm

The article considers a metaheuristic Artificial Ecosystem-based Optimization (AEO) algorithm, which simulates interactions between ecosystem components by creating an initial population of solutions and applying adaptive update strategies, and describes in detail the stages of AEO operation, including the consumption and decomposition phases, as well as different agent behavior strategies. The article introduces the features and advantages of this algorithm.
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Artificial Cooperative Search (ACS) algorithm

Artificial Cooperative Search (ACS) algorithm

Artificial Cooperative Search (ACS) is an innovative method using a binary matrix and multiple dynamic populations based on mutualistic relationships and cooperation to find optimal solutions quickly and accurately. ACS unique approach to predators and prey enables it to achieve excellent results in numerical optimization problems.
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Developing a Replay System — Market simulation (Part 16): New class system

Developing a Replay System — Market simulation (Part 16): New class system

We need to organize our work better. The code is growing, and if this is not done now, then it will become impossible. Let's divide and conquer. MQL5 allows the use of classes which will assist in implementing this task, but for this we need to have some knowledge about classes. Probably the thing that confuses beginners the most is inheritance. In this article, we will look at how to use these mechanisms in a practical and simple way.
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MQL5 Wizard Techniques you should know (Part 07): Dendrograms

MQL5 Wizard Techniques you should know (Part 07): Dendrograms

Data classification for purposes of analysis and forecasting is a very diverse arena within machine learning and it features a large number of approaches and methods. This piece looks at one such approach, namely Agglomerative Hierarchical Classification.
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Developing a Replay System — Market simulation (Part 07): First improvements (II)

Developing a Replay System — Market simulation (Part 07): First improvements (II)

In the previous article, we made some fixes and added tests to our replication system to ensure the best possible stability. We also started creating and using a configuration file for this system.
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Statistical Arbitrage Through Cointegrated Stocks (Part 4): Real-time Model Updating

Statistical Arbitrage Through Cointegrated Stocks (Part 4): Real-time Model Updating

This article describes a simple but comprehensive statistical arbitrage pipeline for trading a basket of cointegrated stocks. It includes a fully functional Python script for data download and storage; correlation, cointegration, and stationarity tests, along with a sample Metatrader 5 Service implementation for database updating, and the respective Expert Advisor. Some design choices are documented here for reference and for helping in the experiment replication.
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Population optimization algorithms: Resistance to getting stuck in local extrema (Part II)

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

We continue our 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. Research results are provided.
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Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (III): Communication Module

Creating a Trading Administrator Panel in MQL5 (Part IX): Code Organization (III): Communication Module

Join us for an in-depth discussion on the latest advancements in MQL5 interface design as we unveil the redesigned Communications Panel and continue our series on building the New Admin Panel using modularization principles. We'll develop the CommunicationsDialog class step by step, thoroughly explaining how to inherit it from the Dialog class. Additionally, we'll leverage arrays and ListView class in our development. Gain actionable insights to elevate your MQL5 development skills—read through the article and join the discussion in the comments section!
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Population optimization algorithms: Simulated Isotropic Annealing (SIA) algorithm. Part II

Population optimization algorithms: Simulated Isotropic Annealing (SIA) algorithm. Part II

The first part was devoted to the well-known and popular algorithm - simulated annealing. We have thoroughly considered its pros and cons. The second part of the article is devoted to the radical transformation of the algorithm, which turns it into a new optimization algorithm - Simulated Isotropic Annealing (SIA).
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MQL5 Wizard Techniques you should know (Part 36): Q-Learning with Markov Chains

MQL5 Wizard Techniques you should know (Part 36): Q-Learning with Markov Chains

Reinforcement Learning is one of the three main tenets in machine learning, alongside supervised learning and unsupervised learning. It is therefore concerned with optimal control, or learning the best long-term policy that will best suit the objective function. It is with this back-drop, that we explore its possible role in informing the learning-process to an MLP of a wizard assembled Expert Advisor.
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Population optimization algorithms: Evolution Strategies, (μ,λ)-ES and (μ+λ)-ES

Population optimization algorithms: Evolution Strategies, (μ,λ)-ES and (μ+λ)-ES

The article considers a group of optimization algorithms known as Evolution Strategies (ES). They are among the very first population algorithms to use evolutionary principles for finding optimal solutions. We will implement changes to the conventional ES variants and revise the test function and test stand methodology for the algorithms.
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Chaos Game Optimization (CGO)

Chaos Game Optimization (CGO)

The article presents a new metaheuristic algorithm, Chaos Game Optimization (CGO), which demonstrates a unique ability to maintain high efficiency when dealing with high-dimensional problems. Unlike most optimization algorithms, CGO not only does not lose, but sometimes even increases performance when scaling a problem, which is its key feature.
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Developing a multi-currency Expert Advisor (Part 7): Selecting a group based on forward period

Developing a multi-currency Expert Advisor (Part 7): Selecting a group based on forward period

Previously, we evaluated the selection of a group of trading strategy instances, with the aim of improving the results of their joint operation, only on the same time period, in which the optimization of individual instances was carried out. Let's see what happens in the forward period.
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Developing a Replay System (Part 47): Chart Trade Project (VI)

Developing a Replay System (Part 47): Chart Trade Project (VI)

Finally, our Chart Trade indicator starts interacting with the EA, allowing information to be transferred interactively. Therefore, in this article, we will improve the indicator, making it functional enough to be used together with any EA. This will allow us to access the Chart Trade indicator and work with it as if it were actually connected with an EA. But we will do it in a much more interesting way than before.
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Matrix Factorization: The Basics

Matrix Factorization: The Basics

Since the goal here is didactic, we will proceed as simply as possible. That is, we will implement only what we need: matrix multiplication. You will see today that this is enough to simulate matrix-scalar multiplication. The most significant difficulty that many people encounter when implementing code using matrix factorization is this: unlike scalar factorization, where in almost all cases the order of the factors does not change the result, this is not the case when using matrices.
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Sigma Score Indicator for MetaTrader 5: A Simple Statistical Anomaly Detector

Sigma Score Indicator for MetaTrader 5: A Simple Statistical Anomaly Detector

Build a practical MetaTrader 5 “Sigma Score” indicator from scratch and learn what it really measures: The z-score of log returns (how many standard deviations the latest move is from the recent average). The article walks through every code block in OnInit(), OnCalculate(), and OnDeinit(), then shows how to interpret thresholds (e.g., ±2) and apply the Sigma Score as a simple “market stress meter” for mean-reversion and momentum trading.
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Data Science and ML (Part 34): Time series decomposition, Breaking the stock market down to the core

Data Science and ML (Part 34): Time series decomposition, Breaking the stock market down to the core

In a world overflowing with noisy and unpredictable data, identifying meaningful patterns can be challenging. In this article, we'll explore seasonal decomposition, a powerful analytical technique that helps separate data into its key components: trend, seasonal patterns, and noise. By breaking data down this way, we can uncover hidden insights and work with cleaner, more interpretable information.
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Fibonacci in Forex (Part I): Examining the Price-Time Relationship

Fibonacci in Forex (Part I): Examining the Price-Time Relationship

How does the market observe Fibonacci-based relationships? This sequence, where each subsequent number is equal to the sum of the two previous ones (1, 1, 2, 3, 5, 8, 13, 21...), not only describes the growth of the rabbit population. We will consider the Pythagorean hypothesis that everything in the world is subject to certain relationships of numbers...
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The case for using a Composite Data Set this Q4 in weighing SPDR XLY's next performance

The case for using a Composite Data Set this Q4 in weighing SPDR XLY's next performance

We consider XLY, SPDR’s consumer discretionary spending ETF and see if with tools in MetaTrader’s IDE we can sift through an array of data sets in selecting what could work with a forecasting model with a forward outlook of not more than a year.
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Category Theory in MQL5 (Part 19): Naturality Square Induction

Category Theory in MQL5 (Part 19): Naturality Square Induction

We continue our look at natural transformations by considering naturality square induction. Slight restraints on multicurrency implementation for experts assembled with the MQL5 wizard mean we are showcasing our data classification abilities with a script. Principle applications considered are price change classification and thus its forecasting.
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Population optimization algorithms: Bird Swarm Algorithm (BSA)

Population optimization algorithms: Bird Swarm Algorithm (BSA)

The article explores the bird swarm-based algorithm (BSA) inspired by the collective flocking interactions of birds in nature. The different search strategies of individuals in BSA, including switching between flight, vigilance and foraging behavior, make this algorithm multifaceted. It uses the principles of bird flocking, communication, adaptability, leading and following to efficiently find optimal solutions.
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Developing a Replay System (Part 72): An Unusual Communication (I)

Developing a Replay System (Part 72): An Unusual Communication (I)

What we create today will be difficult to understand. Therefore, in this article I will only talk about the initial stage. Please read this article carefully, it is an important prerequisite before we proceed to the next step. The purpose of this material is purely didactic as we will only study and master the presented concepts, without practical application.
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Data label for time series mining (Part 5):Apply and Test in EA Using Socket

Data label for time series mining (Part 5):Apply and Test in EA Using Socket

This series of articles introduces several time series labeling methods, which can create data that meets most artificial intelligence models, and targeted data labeling according to needs can make the trained artificial intelligence model more in line with the expected design, improve the accuracy of our model, and even help the model make a qualitative leap!
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MQL5 Wizard Techniques you should know (Part 34): Price-Embedding with an Unconventional RBM

MQL5 Wizard Techniques you should know (Part 34): Price-Embedding with an Unconventional RBM

Restricted Boltzmann Machines are a form of neural network that was developed in the mid 1980s at a time when compute resources were prohibitively expensive. At its onset, it relied on Gibbs Sampling and Contrastive Divergence in order to reduce dimensionality or capture the hidden probabilities/properties over input training data sets. We examine how Backpropagation can perform similarly when the RBM ‘embeds’ prices for a forecasting Multi-Layer-Perceptron.