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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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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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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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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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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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 (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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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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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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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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Integrating MQL5 with data processing packages (Part 4): Big Data Handling

Integrating MQL5 with data processing packages (Part 4): Big Data Handling

Exploring advanced techniques to integrate MQL5 with powerful data processing tools, this part focuses on efficient handling of big data to enhance trading analysis and decision-making.
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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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Reimagining Classic Strategies (Part 14): Multiple Strategy Analysis

Reimagining Classic Strategies (Part 14): Multiple Strategy Analysis

In this article, we continue our exploration of building an ensemble of trading strategies and using the MT5 genetic optimizer to tune the strategy parameters. Today, we analyzed the data in Python, showing our model could better predict which strategy would outperform, achieving higher accuracy than forecasting market returns directly. However, when we tested our application with its statistical models, our performance levels fell dismally. We subsequently discovered that the genetic optimizer unfortunately favored highly correlated strategies, prompting us to revise our method to keep vote weights fixed and focus optimization on indicator settings instead.
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Redefining MQL5 and MetaTrader 5 Indicators

Redefining MQL5 and MetaTrader 5 Indicators

An innovative approach to collecting indicator information in MQL5 enables more flexible and streamlined data analysis by allowing developers to pass custom inputs to indicators for immediate calculations. This approach is particularly useful for algorithmic trading, as it provides enhanced control over the information processed by indicators, moving beyond traditional constraints.
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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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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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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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Permuting price bars in MQL5

Permuting price bars in MQL5

In this article we present an algorithm for permuting price bars and detail how permutation tests can be used to recognize instances where strategy performance has been fabricated to deceive potential buyers of Expert Advisors.
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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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Dynamic mode decomposition applied to univariate time series in MQL5

Dynamic mode decomposition applied to univariate time series in MQL5

Dynamic mode decomposition (DMD) is a technique usually applied to high-dimensional datasets. In this article, we demonstrate the application of DMD on univariate time series, showing its ability to characterize a series as well as make forecasts. In doing so, we will investigate MQL5's built-in implementation of dynamic mode decomposition, paying particular attention to the new matrix method, DynamicModeDecomposition().
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Integrating MQL5 with data processing packages (Part 1): Advanced Data analysis and Statistical Processing

Integrating MQL5 with data processing packages (Part 1): Advanced Data analysis and Statistical Processing

Integration enables seamless workflow where raw financial data from MQL5 can be imported into data processing packages like Jupyter Lab for advanced analysis including statistical testing.
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Statistical Arbitrage Through Cointegrated Stocks (Part 5): Screening

Statistical Arbitrage Through Cointegrated Stocks (Part 5): Screening

This article proposes an asset screening process for a statistical arbitrage trading strategy through cointegrated stocks. The system starts with the regular filtering by economic factors, like asset sector and industry, and finishes with a list of criteria for a scoring system. For each statistical test used in the screening, a respective Python class was developed: Pearson correlation, Engle-Granger cointegration, Johansen cointegration, and ADF/KPSS stationarity. These Python classes are provided along with a personal note from the author about the use of AI assistants for software development.
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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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Singular Spectrum Analysis in MQL5

Singular Spectrum Analysis in MQL5

This article is meant as a guide for those unfamiliar with the concept of Singular Spectrum Analysis and who wish to gain enough understanding to be able to apply the built-in tools available in MQL5.
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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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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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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.
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Introduction to MQL5 (Part 31): Mastering API and WebRequest Function in MQL5 (V)

Introduction to MQL5 (Part 31): Mastering API and WebRequest Function in MQL5 (V)

Learn how to use WebRequest and external API calls to retrieve recent candle data, convert each value into a usable type, and save the information neatly in a table format. This step lays the groundwork for building an indicator that visualizes the data in candle format.
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Developing a Replay System (Part 62): Playing the service (III)

Developing a Replay System (Part 62): Playing the service (III)

In this article, we will begin to address the issue of tick excess that can impact application performance when using real data. This excess often interferes with the correct timing required to construct a one-minute bar in the appropriate window.
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Category Theory in MQL5 (Part 21): Natural Transformations with LDA

Category Theory in MQL5 (Part 21): Natural Transformations with LDA

This article, the 21st in our series, continues with a look at Natural Transformations and how they can be implemented using linear discriminant analysis. We present applications of this in a signal class format, like in the previous article.
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The Group Method of Data Handling: Implementing the Combinatorial Algorithm in MQL5

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

In this article we continue our exploration of the Group Method of Data Handling family of algorithms, with the implementation of the Combinatorial Algorithm along with its refined incarnation, the Combinatorial Selective Algorithm in MQL5.
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Visualizing deals on a chart (Part 1): Selecting a period for analysis

Visualizing deals on a chart (Part 1): Selecting a period for analysis

Here we are going to develop a script from scratch that simplifies unloading print screens of deals for analyzing trading entries. All the necessary information on a single deal is to be conveniently displayed on one chart with the ability to draw different timeframes.
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Developing a Replay System (Part 50): Things Get Complicated (II)

Developing a Replay System (Part 50): Things Get Complicated (II)

We will solve the chart ID problem and at the same time we will begin to provide the user with the ability to use a personal template for the analysis and simulation of the desired asset. The materials presented here are for didactic purposes only and should in no way be considered as an application for any purpose other than studying and mastering the concepts presented.
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ALGLIB library optimization methods (Part I)

ALGLIB library optimization methods (Part I)

In this article, we will get acquainted with the ALGLIB library optimization methods for MQL5. The article includes simple and clear examples of using ALGLIB to solve optimization problems, which will make mastering the methods as accessible as possible. We will take a detailed look at the connection of such algorithms as BLEIC, L-BFGS and NS, and use them to solve a simple test problem.
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Resampling techniques for prediction and classification assessment in MQL5

Resampling techniques for prediction and classification assessment in MQL5

In this article, we will explore and implement, methods for assessing model quality that utilize a single dataset as both training and validation sets.
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Bivariate Copulae in MQL5 (Part 2): Implementing Archimedean copulae in MQL5

Bivariate Copulae in MQL5 (Part 2): Implementing Archimedean copulae in MQL5

In the second installment of the series, we discuss the properties of bivariate Archimedean copulae and their implementation in MQL5. We also explore applying copulae to the development of a simple pairs trading strategy.
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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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Artificial Bee Hive Algorithm (ABHA): Theory and methods

Artificial Bee Hive Algorithm (ABHA): Theory and methods

In this article, we will consider the Artificial Bee Hive Algorithm (ABHA) developed in 2009. The algorithm is aimed at solving continuous optimization problems. We will look at how ABHA draws inspiration from the behavior of a bee colony, where each bee has a unique role that helps them find resources more efficiently.