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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Market Simulation (Part 13): Sockets (VII)

Market Simulation (Part 13): Sockets (VII)

When we develop something in xlwings or any other package that allows reading and writing directly to Excel, we must note that all programs, functions, or procedures execute and then complete their task. They do not remain in a loop, no matter how hard we try to do things differently.
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MQL5 Wizard Techniques you should know (Part 32): Regularization

MQL5 Wizard Techniques you should know (Part 32): Regularization

Regularization is a form of penalizing the loss function in proportion to the discrete weighting applied throughout the various layers of a neural network. We look at the significance, for some of the various regularization forms, this can have in test runs with a wizard assembled Expert Advisor.
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Statistical Arbitrage Through Cointegrated Stocks (Part 3): Database Setup

Statistical Arbitrage Through Cointegrated Stocks (Part 3): Database Setup

This article presents a sample MQL5 Service implementation for updating a newly created database used as source for data analysis and for trading a basket of cointegrated stocks. The rationale behind the database design is explained in detail and the data dictionary is documented for reference. MQL5 and Python scripts are provided for the database creation, schema initialization, and market data insertion.
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Self Optimizing Expert Advisors in MQL5 (Part 12): Building Linear Classifiers Using Matrix Factorization

Self Optimizing Expert Advisors in MQL5 (Part 12): Building Linear Classifiers Using Matrix Factorization

This article explores the powerful role of matrix factorization in algorithmic trading, specifically within MQL5 applications. From regression models to multi-target classifiers, we walk through practical examples that demonstrate how easily these techniques can be integrated using built-in MQL5 functions. Whether you're predicting price direction or modeling indicator behavior, this guide lays a strong foundation for building intelligent trading systems using matrix methods.
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Analyzing binary code of prices on the exchange (Part II): Converting to BIP39 and writing GPT model

Analyzing binary code of prices on the exchange (Part II): Converting to BIP39 and writing GPT model

Continuing tries to decipher price movements... What about linguistic analysis of the "market dictionary" that we get by converting the binary price code to BIP39? In this article, we will delve into an innovative approach to exchange data analysis and consider how modern natural language processing techniques can be applied to the market language.
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Developing a Replay System (Part 29): Expert Advisor project — C_Mouse class (III)

Developing a Replay System (Part 29): Expert Advisor project — C_Mouse class (III)

After improving the C_Mouse class, we can focus on creating a class designed to create a completely new framework fr our analysis. We will not use inheritance or polymorphism to create this new class. Instead, we will change, or better said, add new objects to the price line. That's what we will do in this article. In the next one, we will look at how to change the analysis. All this will be done without changing the code of the C_Mouse class. Well, actually, it would be easier to achieve this using inheritance or polymorphism. However, there are other methods to achieve the same result.
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Developing a Replay System (Part 46): Chart Trade Project (V)

Developing a Replay System (Part 46): Chart Trade Project (V)

Tired of wasting time searching for that very file that you application needs in order to work? How about including everything in the executable? This way you won't have to search for the things. I know that many people use this form of distribution and storage, but there is a much more suitable way. At least as far as the distribution of executable files and their storage is concerned. The method that will be presented here can be very useful, since you can use MetaTrader 5 itself as an excellent assistant, as well as MQL5. Furthermore, it is not that difficult to understand.
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Developing a Replay System (Part 40): Starting the second phase (I)

Developing a Replay System (Part 40): Starting the second phase (I)

Today we'll talk about the new phase of the replay/simulator system. At this stage, the conversation will become truly interesting and quite rich in content. I strongly recommend that you read the article carefully and use the links provided in it. This will help you understand the content better.
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Developing a Replay System (Part 43): Chart Trade Project (II)

Developing a Replay System (Part 43): Chart Trade Project (II)

Most people who want or dream of learning to program don't actually have a clue what they're doing. Their activity consists of trying to create things in a certain way. However, programming is not about tailoring suitable solutions. Doing it this way can create more problems than solutions. Here we will be doing something more advanced and therefore different.
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MQL5 Wizard Techniques you should know (Part 55): SAC with Prioritized Experience Replay

MQL5 Wizard Techniques you should know (Part 55): SAC with Prioritized Experience Replay

Replay buffers in Reinforcement Learning are particularly important with off-policy algorithms like DQN or SAC. This then puts the spotlight on the sampling process of this memory-buffer. While default options with SAC, for instance, use random selection from this buffer, Prioritized Experience Replay buffers fine tune this by sampling from the buffer based on a TD-score. We review the importance of Reinforcement Learning, and, as always, examine just this hypothesis (not the cross-validation) in a wizard assembled Expert Advisor.
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Population optimization algorithms: Boids Algorithm

Population optimization algorithms: Boids Algorithm

The article considers Boids algorithm based on unique examples of animal flocking behavior. In turn, the Boids algorithm serves as the basis for the creation of the whole class of algorithms united under the name "Swarm Intelligence".
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Data Science and ML (Part 36): Dealing with Biased Financial Markets

Data Science and ML (Part 36): Dealing with Biased Financial Markets

Financial markets are not perfectly balanced. Some markets are bullish, some are bearish, and some exhibit some ranging behaviors indicating uncertainty in either direction, this unbalanced information when used to train machine learning models can be misleading as the markets change frequently. In this article, we are going to discuss several ways to tackle this issue.
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Quantitative Analysis of Trends: Collecting Statistics in Python

Quantitative Analysis of Trends: Collecting Statistics in Python

What is quantitative trend analysis in the Forex market? We collect statistics on trends, their magnitude and distribution across the EURUSD currency pair. How quantitative trend analysis can help you create a profitable trading expert advisor.
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Market Simulation (Part 04): Creating the C_Orders Class (I)

Market Simulation (Part 04): Creating the C_Orders Class (I)

In this article, we will start creating the C_Orders class to be able to send orders to the trading server. We'll do this little by little, as our goal is to explain in detail how this will happen through the messaging system.
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Developing a Replay System (Part 67): Refining the Control Indicator

Developing a Replay System (Part 67): Refining the Control Indicator

In this article, we'll look at what can be achieved with a little code refinement. This refinement is aimed at simplifying our code, making more use of MQL5 library calls and, above all, making it much more stable, secure and easy to use in other projects that we may develop in the future.
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Capital management in trading and the trader's home accounting program with a database

Capital management in trading and the trader's home accounting program with a database

How can a trader manage capital? How can a trader and investor keep track of expenses, income, assets, and liabilities? I am not just going to introduce you to accounting software; I am going to show you a tool that might become your reliable financial navigator in the stormy sea of trading.
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Swap Arbitrage in Forex: Building a Synthetic Portfolio and Generating a Consistent Swap Flow

Swap Arbitrage in Forex: Building a Synthetic Portfolio and Generating a Consistent Swap Flow

Do you want to know how to benefit from the difference in interest rates? This article considers how to use swap arbitrage in Forex to earn stable profit every night, creating a portfolio that is resistant to market fluctuations.
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Population optimization algorithms: Spiral Dynamics Optimization (SDO) algorithm

Population optimization algorithms: Spiral Dynamics Optimization (SDO) algorithm

The article presents an optimization algorithm based on the patterns of constructing spiral trajectories in nature, such as mollusk shells - the spiral dynamics optimization (SDO) algorithm. I have thoroughly revised and modified the algorithm proposed by the authors. The article will consider the necessity of these changes.
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Ensemble methods to enhance numerical predictions in MQL5

Ensemble methods to enhance numerical predictions in MQL5

In this article, we present the implementation of several ensemble learning methods in MQL5 and examine their effectiveness across different scenarios.
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Animal Migration Optimization (AMO) algorithm

Animal Migration Optimization (AMO) algorithm

The article is devoted to the AMO algorithm, which models the seasonal migration of animals in search of optimal conditions for life and reproduction. The main features of AMO include the use of topological neighborhood and a probabilistic update mechanism, which makes it easy to implement and flexible for various optimization tasks.
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Creating a Trading Administrator Panel in MQL5 (Part XI): Modern feature communications interface (I)

Creating a Trading Administrator Panel in MQL5 (Part XI): Modern feature communications interface (I)

Today, we are focusing on the enhancement of the Communications Panel messaging interface to align with the standards of modern, high-performing communication applications. This improvement will be achieved by updating the CommunicationsDialog class. Join us in this article and discussion as we explore key insights and outline the next steps in advancing interface programming using MQL5.
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Most notable Artificial Cooperative Search algorithm modifications (ACSm)

Most notable Artificial Cooperative Search algorithm modifications (ACSm)

Here we will consider the evolution of the ACS algorithm: three modifications aimed at improving the convergence characteristics and the algorithm efficiency. Transformation of one of the leading optimization algorithms. From matrix modifications to revolutionary approaches regarding population formation.
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Economic forecasts: Exploring the Python potential

Economic forecasts: Exploring the Python potential

How to use World Bank economic data for forecasts? What happens when you combine AI models and economics?
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Successful Restaurateur Algorithm (SRA)

Successful Restaurateur Algorithm (SRA)

Successful Restaurateur Algorithm (SRA) is an innovative optimization method inspired by restaurant business management principles. Unlike traditional approaches, SRA does not discard weak solutions, but improves them by combining with elements of successful ones. The algorithm shows competitive results and offers a fresh perspective on balancing exploration and exploitation in optimization problems.
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Forecasting exchange rates using classic machine learning methods: Logit and Probit models

Forecasting exchange rates using classic machine learning methods: Logit and Probit models

In the article, an attempt is made to build a trading EA for predicting exchange rate quotes. The algorithm is based on classical classification models - logistic and probit regression. The likelihood ratio criterion is used as a filter for trading signals.
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Developing a Replay System (Part 33): Order System (II)

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

Today we will continue to develop the order system. As you will see, we will be massively reusing what has already been shown in other articles. Nevertheless, you will receive a small reward in this article. First, we will develop a system that can be used with a real trading server, both from a demo account or from a real one. We will make extensive use of the MetaTrader 5 platform, which will provide us with all the necessary support from the beginning.
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Developing a Replay System (Part 69): Getting the Time Right (II)

Developing a Replay System (Part 69): Getting the Time Right (II)

Today we will look at why we need the iSpread feature. At the same time, we will understand how the system informs us about the remaining time of the bar when there is not a single tick available for it. 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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Causal analysis of time series using transfer entropy

Causal analysis of time series using transfer entropy

In this article, we discuss how statistical causality can be applied to identify predictive variables. We will explore the link between causality and transfer entropy, as well as present MQL5 code for detecting directional transfers of information between two variables.
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Spurious Regressions in Python

Spurious Regressions in Python

Spurious regressions occur when two time series exhibit a high degree of correlation purely by chance, leading to misleading results in regression analysis. In such cases, even though variables may appear to be related, the correlation is coincidental and the model may be unreliable.
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Creating a Trading Administrator Panel in MQL5 (Part X): External resource-based interface

Creating a Trading Administrator Panel in MQL5 (Part X): External resource-based interface

Today, we are harnessing the capabilities of MQL5 to utilize external resources—such as images in the BMP format—to create a uniquely styled home interface for the Trading Administrator Panel. The strategy demonstrated here is particularly useful when packaging multiple resources, including images, sounds, and more, for streamlined distribution. Join us in this discussion as we explore how these features are implemented to deliver a modern and visually appealing interface for our New_Admin_Panel EA.
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Tracking Account Dynamics: Balance, Equity, and Floating P/L Visualization in MQL5

Tracking Account Dynamics: Balance, Equity, and Floating P/L Visualization in MQL5

Create a custom MT5 indicator that processes the entire deal history and plots starting balance, balance, equity, and floating P/L as continuous curves. It updates per bar, aggregates positions across symbols, and avoids external dependencies through local caching. Use it to inspect equity–balance divergence, realized vs. unrealized results, and the timing of risk deployment.
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Anarchic Society Optimization (ASO) algorithm

Anarchic Society Optimization (ASO) algorithm

In this article, we will get acquainted with the Anarchic Society Optimization (ASO) algorithm and discuss how an algorithm based on the irrational and adventurous behavior of participants in an anarchic society (an anomalous system of social interaction free from centralized power and various kinds of hierarchies) is able to explore the solution space and avoid the traps of local optimum. The article presents a unified ASO structure applicable to both continuous and discrete problems.
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Statistical Arbitrage Through Cointegrated Stocks (Part 8): Rolling Windows Eigenvector Comparison for Portfolio Rebalancing

Statistical Arbitrage Through Cointegrated Stocks (Part 8): Rolling Windows Eigenvector Comparison for Portfolio Rebalancing

This article proposes using Rolling Windows Eigenvector Comparison for early imbalance diagnostics and portfolio rebalancing in a mean-reversion statistical arbitrage strategy based on cointegrated stocks. It contrasts this technique with traditional In-Sample/Out-of-Sample ADF validation, showing that eigenvector shifts can signal the need for rebalancing even when IS/OOS ADF still indicates a stationary spread. While the method is intended mainly for live trading monitoring, the article concludes that eigenvector comparison could also be integrated into the scoring system—though its actual contribution to performance remains to be tested.
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Chemical reaction optimization (CRO) algorithm (Part I): Process chemistry in optimization

Chemical reaction optimization (CRO) algorithm (Part I): Process chemistry in optimization

In the first part of this article, we will dive into the world of chemical reactions and discover a new approach to optimization! Chemical reaction optimization (CRO) uses principles derived from the laws of thermodynamics to achieve efficient results. We will reveal the secrets of decomposition, synthesis and other chemical processes that became the basis of this innovative method.
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Biological neuron for forecasting financial time series

Biological neuron for forecasting financial time series

We will build a biologically correct system of neurons for time series forecasting. The introduction of a plasma-like environment into the neural network architecture creates a kind of "collective intelligence," where each neuron influences the system's operation not only through direct connections, but also through long-range electromagnetic interactions. Let's see how the neural brain modeling system will perform in the market.
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Category Theory in MQL5 (Part 12): Orders

Category Theory in MQL5 (Part 12): Orders

This article which is part of a series that follows Category Theory implementation of Graphs in MQL5, delves in Orders. We examine how concepts of Order-Theory can support monoid sets in informing trade decisions by considering two major ordering types.
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Hybridization of population algorithms. Sequential and parallel structures

Hybridization of population algorithms. Sequential and parallel structures

Here we will dive into the world of hybridization of optimization algorithms by looking at three key types: strategy mixing, sequential and parallel hybridization. We will conduct a series of experiments combining and testing relevant optimization algorithms.
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An introduction to Receiver Operating Characteristic curves

An introduction to Receiver Operating Characteristic curves

ROC curves are graphical representations used to evaluate the performance of classifiers. Despite ROC graphs being relatively straightforward, there exist common misconceptions and pitfalls when using them in practice. This article aims to provide an introduction to ROC graphs as a tool for practitioners seeking to understand classifier performance evaluation.
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Ordinal Encoding for Nominal Variables

Ordinal Encoding for Nominal Variables

In this article, we discuss and demonstrate how to convert nominal predictors into numerical formats that are suitable for machine learning algorithms, using both Python and MQL5.
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Integrating MQL5 with data processing packages (Part 3): Enhanced Data Visualization

Integrating MQL5 with data processing packages (Part 3): Enhanced Data Visualization

In this article, we will perform Enhanced Data Visualization by going beyond basic charts by incorporating features like interactivity, layered data, and dynamic elements, enabling traders to explore trends, patterns, and correlations more effectively.