Articles on data analysis and statistics in MQL5

icon

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.

Add a new article
latest | best
preview
Developing a Replay System (Part 77): New Chart Trade (IV)

Developing a Replay System (Part 77): New Chart Trade (IV)

In this article, we will cover some of the measures and precautions to consider when creating a communication protocol. These are pretty simple and straightforward things, so we won't go into too much detail in this article. But to understand what will happen, you need to understand the content of the article.
preview
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.
preview
Creating Custom Indicators in MQL5 (Part 8): Adding Volume Integration for Deeper Market Profile Analysis

Creating Custom Indicators in MQL5 (Part 8): Adding Volume Integration for Deeper Market Profile Analysis

In this article, we enhance the hybrid Time Price Opportunity (TPO) market profile indicator in MQL5 by integrating volume data to calculate volume-based point of control, value areas, and volume-weighted average price with customizable highlighting options. The system introduces advanced features like initial balance detection, key level extension lines, split profiles, and alternative TPO characters such as squares or circles for improved visual analysis across multiple timeframes.
preview
Dialectic Search (DA)

Dialectic Search (DA)

The article introduces the dialectical algorithm (DA), a new global optimization method inspired by the philosophical concept of dialectics. The algorithm exploits a unique division of the population into speculative and practical thinkers. Testing shows impressive performance of up to 98% on low-dimensional problems and overall efficiency of 57.95%. The article explains these metrics and presents a detailed description of the algorithm and the results of experiments on different types of functions.
preview
MQL5 Wizard Techniques you should know (Part 31): Selecting the Loss Function

MQL5 Wizard Techniques you should know (Part 31): Selecting the Loss Function

Loss Function is the key metric of machine learning algorithms that provides feedback to the training process by quantifying how well a given set of parameters are performing when compared to their intended target. We explore the various formats of this function in an MQL5 custom wizard class.
preview
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.
preview
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!
preview
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.
preview
Coral Reefs Optimization (CRO)

Coral Reefs Optimization (CRO)

The article presents a comprehensive analysis of the Coral Reef Optimization (CRO) algorithm, a metaheuristic method inspired by the biological processes of coral reef formation and development. The algorithm models key aspects of coral evolution: broadcast spawning, brooding, larval settlement, asexual reproduction, and competition for limited reef space. Particular attention is paid to the improved version of the algorithm.
preview
Mining Central Bank Balance Sheet Data to Get a Picture of Global Liquidity

Mining Central Bank Balance Sheet Data to Get a Picture of Global Liquidity

Mining central bank balance sheet data provides a picture of global liquidity in the Forex market and key currencies. We combine data from the Fed, ECB, BOJ and PBoC into a composite index and use machine learning to uncover hidden patterns. This approach turns raw data into real trading signals by combining fundamental and technical analysis.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
Developing a Replay System (Part 36): Making Adjustments (II)

Developing a Replay System (Part 36): Making Adjustments (II)

One of the things that can make our lives as programmers difficult is assumptions. In this article, I will show you how dangerous it is to make assumptions: both in MQL5 programming, where you assume that the type will have a certain value, and in MetaTrader 5, where you assume that different servers work the same.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
Low-Frequency Quantitative Strategies in Metatrader 5: (Part 1) Setting Up An OLAP-Friendly Data Store

Low-Frequency Quantitative Strategies in Metatrader 5: (Part 1) Setting Up An OLAP-Friendly Data Store

The article outlines a practical data pipeline for quantitative analysis based on Parquet storage, Hive-style partitions, and DuckDB. It details migrating selected SQLite tables to Parquet, structuring market data by source, symbol, timeframe, and date, and querying it with SQL window functions. A Golden Cross example illustrates cross‑symbol evaluation of forward returns. Accompanying Python scripts handle data download, conversion, and execution.
preview
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.
preview
Statistical Arbitrage Through Cointegrated Stocks (Part 7): Scoring System 2

Statistical Arbitrage Through Cointegrated Stocks (Part 7): Scoring System 2

This article describes two additional scoring criteria used for selection of baskets of stocks to be traded in mean-reversion strategies, more specifically, in cointegration based statistical arbitrage. It complements a previous article where liquidity and strength of the cointegration vectors were presented, along with the strategic criteria of timeframe and lookback period, by including the stability of the cointegration vectors and the time to mean reversion (half-time). The article includes the commented results of a backtest with the new filters applied and the files required for its reproduction are also provided.
preview
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!
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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().
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.