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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Data Science and Machine Learning (Part 05): Decision Trees

Data Science and Machine Learning (Part 05): Decision Trees

Decision trees imitate the way humans think to classify data. Let's see how to build trees and use them to classify and predict some data. The main goal of the decision trees algorithm is to separate the data with impurity and into pure or close to nodes.
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Population optimization algorithms: Ant Colony Optimization (ACO)

Population optimization algorithms: Ant Colony Optimization (ACO)

This time I will analyze the Ant Colony optimization algorithm. The algorithm is very interesting and complex. In the article, I make an attempt to create a new type of ACO.
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Brute force approach to patterns search (Part VI): Cyclic optimization

Brute force approach to patterns search (Part VI): Cyclic optimization

In this article I will show the first part of the improvements that allowed me not only to close the entire automation chain for MetaTrader 4 and 5 trading, but also to do something much more interesting. From now on, this solution allows me to fully automate both creating EAs and optimization, as well as to minimize labor costs for finding effective trading configurations.
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Timeseries in DoEasy library (part 55): Indicator collection class

Timeseries in DoEasy library (part 55): Indicator collection class

The article continues developing indicator object classes and their collections. For each indicator object create its description and correct collection class for error-free storage and getting indicator objects from the collection list.
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Metamodels in machine learning and trading: Original timing of trading orders

Metamodels in machine learning and trading: Original timing of trading orders

Metamodels in machine learning: Auto creation of trading systems with little or no human intervention — The model decides when and how to trade on its own.
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Rebuy algorithm: Multicurrency trading simulation

Rebuy algorithm: Multicurrency trading simulation

In this article, we will create a mathematical model for simulating multicurrency pricing and complete the study of the diversification principle as part of the search for mechanisms to increase the trading efficiency, which I started in the previous article with theoretical calculations.
Other classes in DoEasy library (Part 68): Chart window object class and indicator object classes in the chart window
Other classes in DoEasy library (Part 68): Chart window object class and indicator object classes in the chart window

Other classes in DoEasy library (Part 68): Chart window object class and indicator object classes in the chart window

In this article, I will continue the development of the chart object class. I will add the list of chart window objects featuring the lists of available indicators.
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From Novice to Expert: Demystifying Hidden Fibonacci Retracement Levels

From Novice to Expert: Demystifying Hidden Fibonacci Retracement Levels

In this article, we explore a data-driven approach to discovering and validating non-standard Fibonacci retracement levels that markets may respect. We present a complete workflow tailored for implementation in MQL5, beginning with data collection and bar or swing detection, and extending through clustering, statistical hypothesis testing, backtesting, and integration into an MetaTrader 5 Fibonacci tool. The goal is to create a reproducible pipeline that transforms anecdotal observations into statistically defensible trading signals.
One-Minute Data Modelling Quality Rating
One-Minute Data Modelling Quality Rating

One-Minute Data Modelling Quality Rating

One-Minute Data Modelling Quality Rating
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Developing a robot in Python and MQL5 (Part 1): Data preprocessing

Developing a robot in Python and MQL5 (Part 1): Data preprocessing

Developing a trading robot based on machine learning: A detailed guide. The first article in the series deals with collecting and preparing data and features. The project is implemented using the Python programming language and libraries, as well as the MetaTrader 5 platform.
Other classes in DoEasy library (Part 71): Chart object collection events
Other classes in DoEasy library (Part 71): Chart object collection events

Other classes in DoEasy library (Part 71): Chart object collection events

In this article, I will create the functionality for tracking some chart object events — adding/removing symbol charts and chart subwindows, as well as adding/removing/changing indicators in chart windows.
Continuous futures contracts in MetaTrader 5
Continuous futures contracts in MetaTrader 5

Continuous futures contracts in MetaTrader 5

A short life span of futures contracts complicates their technical analysis. It is difficult to technically analyze short charts. For example, number of bars on the day chart of the UX-9.13 Ukrainian Stock index future is more than 100. Therefore, trader creates synthetic long futures contracts. This article explains how to splice futures contracts with different dates in the MetaTrader 5 terminal.
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The price movement model and its main provisions (Part 2): Probabilistic price field evolution equation and the occurrence of the observed random walk

The price movement model and its main provisions (Part 2): Probabilistic price field evolution equation and the occurrence of the observed random walk

The article considers the probabilistic price field evolution equation and the upcoming price spike criterion. It also reveals the essence of price values on charts and the mechanism for the occurrence of a random walk of these values.
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Developing a trading Expert Advisor from scratch (Part 16): Accessing data on the web (II)

Developing a trading Expert Advisor from scratch (Part 16): Accessing data on the web (II)

Knowing how to input data from the Web into an Expert Advisor is not so obvious. It is not so easy to do without understanding all the possibilities offered by MetaTrader 5.
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Building a Trading System (Part 1): A Quantitative Approach

Building a Trading System (Part 1): A Quantitative Approach

Many traders evaluate strategies based on short-term performance, often abandoning profitable systems too early. Long-term profitability, however, depends on positive expectancy through optimized win rate and risk-reward ratio, along with disciplined position sizing. These principles can be validated using Monte Carlo simulation in Python with back-tested metrics to assess whether a strategy is robust or likely to fail over time.
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Price Action Analysis Toolkit Development (Part 13): RSI Sentinel Tool

Price Action Analysis Toolkit Development (Part 13): RSI Sentinel Tool

Price action can be effectively analyzed by identifying divergences, with technical indicators such as the RSI providing crucial confirmation signals. In the article below, we explain how automated RSI divergence analysis can identify trend continuations and reversals, thereby offering valuable insights into market sentiment.
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Developing a trading Expert Advisor from scratch (Part 15): Accessing data on the web (I)

Developing a trading Expert Advisor from scratch (Part 15): Accessing data on the web (I)

How to access online data via MetaTrader 5? There are a lot of websites and places on the web, featuring a huge amount information. What you need to know is where to look and how best to use this information.
Other classes in DoEasy library (Part 69): Chart object collection class
Other classes in DoEasy library (Part 69): Chart object collection class

Other classes in DoEasy library (Part 69): Chart object collection class

With this article, I start the development of the chart object collection class. The class will store the collection list of chart objects with their subwindows and indicators providing the ability to work with any selected charts and their subwindows or with a list of several charts at once.
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Timeseries in DoEasy library (part 49): Multi-period multi-symbol multi-buffer standard indicators

Timeseries in DoEasy library (part 49): Multi-period multi-symbol multi-buffer standard indicators

In the current article, I will improve the library classes to implement the ability to develop multi-symbol multi-period standard indicators requiring several indicator buffers to display their data.
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Reimagining Classic Strategies (Part 18): Searching For Candlestick Patterns

Reimagining Classic Strategies (Part 18): Searching For Candlestick Patterns

This article helps new community members search for and discover their own candlestick patterns. Describing these patterns can be daunting, as it requires manually searching and creatively identifying improvements. Here, we introduce the engulfing candlestick pattern and show how it can be enhanced for more profitable trading applications.
Mountain or Iceberg charts
Mountain or Iceberg charts

Mountain or Iceberg charts

How do you like the idea of adding a new chart type to the MetaTrader 5 platform? Some people say it lacks a few things that other platforms offer. But the truth is, MetaTrader 5 is a very practical platform as it allows you to do things that can't be done (or at least can't be done easily) in many other platforms.
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Forecasting with ARIMA models in MQL5

Forecasting with ARIMA models in MQL5

In this article we continue the development of the CArima class for building ARIMA models by adding intuitive methods that enable forecasting.
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The price movement model and its main provisions. (Part 3): Calculating optimal parameters of stock exchange speculations

The price movement model and its main provisions. (Part 3): Calculating optimal parameters of stock exchange speculations

Within the framework of the engineering approach developed by the author based on the probability theory, the conditions for opening a profitable position are found and the optimal (profit-maximizing) take profit and stop loss values are calculated.
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MetaTrader 5 Machine Learning Blueprint (Part 3): Trend-Scanning Labeling Method

MetaTrader 5 Machine Learning Blueprint (Part 3): Trend-Scanning Labeling Method

We have built a robust feature engineering pipeline using proper tick-based bars to eliminate data leakage and solved the critical problem of labeling with meta-labeled triple-barrier signals. This installment covers the advanced labeling technique, trend-scanning, for adaptive horizons. After covering the theory, an example shows how trend-scanning labels can be used with meta-labeling to improve on the classic moving average crossover strategy.
Timeseries in DoEasy library (part 44): Collection class of indicator buffer objects
Timeseries in DoEasy library (part 44): Collection class of indicator buffer objects

Timeseries in DoEasy library (part 44): Collection class of indicator buffer objects

The article deals with creating a collection class of indicator buffer objects. I am going to test the ability to create and work with any number of buffers for indicators (the maximum number of buffers that can be created in MQL indicators is 512).
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MetaTrader 5 Machine Learning Blueprint (Part 1): Data Leakage and Timestamp Fixes

MetaTrader 5 Machine Learning Blueprint (Part 1): Data Leakage and Timestamp Fixes

Before we can even begin to make use of ML in our trading on MetaTrader 5, it’s crucial to address one of the most overlooked pitfalls—data leakage. This article unpacks how data leakage, particularly the MetaTrader 5 timestamp trap, can distort our model's performance and lead to unreliable trading signals. By diving into the mechanics of this issue and presenting strategies to prevent it, we pave the way for building robust machine learning models that deliver trustworthy predictions in live trading environments.
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Forex arbitrage trading: A simple synthetic market maker bot to get started

Forex arbitrage trading: A simple synthetic market maker bot to get started

Today we will take a look at my first arbitrage robot — a liquidity provider (if you can call it that) for synthetic assets. Currently, this bot is successfully operating as a module in a large machine learning system, but I pulled up an old Forex arbitrage robot from the cloud, so let's take a look at it and think about what we can do with it today.
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Data Science and Machine Learning (Part 23): Why LightGBM and XGBoost outperform a lot of AI models?

Data Science and Machine Learning (Part 23): Why LightGBM and XGBoost outperform a lot of AI models?

These advanced gradient-boosted decision tree techniques offer superior performance and flexibility, making them ideal for financial modeling and algorithmic trading. Learn how to leverage these tools to optimize your trading strategies, improve predictive accuracy, and gain a competitive edge in the financial markets.
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Neural networks made easy (Part 19): Association rules using MQL5

Neural networks made easy (Part 19): Association rules using MQL5

We continue considering association rules. In the previous article, we have discussed theoretical aspect of this type of problem. In this article, I will show the implementation of the FP Growth method using MQL5. We will also test the implemented solution using real data.
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Price Action Analysis Toolkit Development (Part 42): Interactive Chart Testing with Button Logic and Statistical Levels

Price Action Analysis Toolkit Development (Part 42): Interactive Chart Testing with Button Logic and Statistical Levels

In a world where speed and precision matter, analysis tools need to be as smart as the markets we trade. This article presents an EA built on button logic—an interactive system that instantly transforms raw price data into meaningful statistical levels. With a single click, it calculates and displays mean, deviation, percentiles, and more, turning advanced analytics into clear on-chart signals. It highlights the zones where price is most likely to bounce, retrace, or break, making analysis both faster and more practical.
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Price Action Analysis Toolkit Development (Part 17): TrendLoom EA Tool

Price Action Analysis Toolkit Development (Part 17): TrendLoom EA Tool

As a price action observer and trader, I've noticed that when a trend is confirmed by multiple timeframes, it usually continues in that direction. What may vary is how long the trend lasts, and this depends on the type of trader you are, whether you hold positions for the long term or engage in scalping. The timeframes you choose for confirmation play a crucial role. Check out this article for a quick, automated system that helps you analyze the overall trend across different timeframes with just a button click or regular updates.
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Population optimization algorithms: Bacterial Foraging Optimization (BFO)

Population optimization algorithms: Bacterial Foraging Optimization (BFO)

E. coli bacterium foraging strategy inspired scientists to create the BFO optimization algorithm. The algorithm contains original ideas and promising approaches to optimization and is worthy of further study.
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Price Action Analysis Toolkit Development (Part 46): Designing an Interactive Fibonacci Retracement EA with Smart Visualization in MQL5

Price Action Analysis Toolkit Development (Part 46): Designing an Interactive Fibonacci Retracement EA with Smart Visualization in MQL5

Fibonacci tools are among the most popular instruments used by technical analysts. In this article, we’ll build an Interactive Fibonacci EA that draws retracement and extension levels that react dynamically to price movement, delivering real‑time alerts, stylish lines, and a scrolling news‑style headline. Another key advantage of this EA is flexibility; you can manually type the high (A) and low (B) swing values directly on the chart, giving you exact control over the market range you want to analyze.
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Data Science and Machine Learning (Part 24): Forex Time series Forecasting Using Regular AI Models

Data Science and Machine Learning (Part 24): Forex Time series Forecasting Using Regular AI Models

In the forex markets It is very challenging to predict the future trend without having an idea of the past. Very few machine learning models are capable of making the future predictions by considering past values. In this article, we are going to discuss how we can use classical(Non-time series) Artificial Intelligence models to beat the market
Selection and navigation utility in MQL5 and MQL4: Adding "homework" tabs and saving graphical objects
Selection and navigation utility in MQL5 and MQL4: Adding "homework" tabs and saving graphical objects

Selection and navigation utility in MQL5 and MQL4: Adding "homework" tabs and saving graphical objects

In this article, we are going to expand the capabilities of the previously created utility by adding tabs for selecting the symbols we need. We will also learn how to save graphical objects we have created on the specific symbol chart, so that we do not have to constantly create them again. Besides, we will find out how to work only with symbols that have been preliminarily selected using a specific website.
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Developing Trend Trading Strategies Using Machine Learning

Developing Trend Trading Strategies Using Machine Learning

This study introduces a novel methodology for the development of trend-following trading strategies. This section describes the process of annotating training data and using it to train classifiers. This process yields fully operational trading systems designed to run on MetaTrader 5.
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Category Theory in MQL5 (Part 1)

Category Theory in MQL5 (Part 1)

Category Theory is a diverse and expanding branch of Mathematics which as of yet is relatively uncovered in the MQL community. These series of articles look to introduce and examine some of its concepts with the overall goal of establishing an open library that attracts comments and discussion while hopefully furthering the use of this remarkable field in Traders' strategy development.
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High frequency arbitrage trading system in Python using MetaTrader 5

High frequency arbitrage trading system in Python using MetaTrader 5

In this article, we will create an arbitration system that remains legal in the eyes of brokers, creates thousands of synthetic prices on the Forex market, analyzes them, and successfully trades for profit.
Prices in DoEasy library (part 61): Collection of symbol tick series
Prices in DoEasy library (part 61): Collection of symbol tick series

Prices in DoEasy library (part 61): Collection of symbol tick series

Since a program may use different symbols in its work, a separate list should be created for each of them. In this article, I will combine such lists into a tick data collection. In fact, this will be a regular list based on the class of dynamic array of pointers to instances of CObject class and its descendants of the Standard library.
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Parallel Particle Swarm Optimization

Parallel Particle Swarm Optimization

The article describes a method of fast optimization using the particle swarm algorithm. It also presents the method implementation in MQL, which is ready for use both in single-threaded mode inside an Expert Advisor and in a parallel multi-threaded mode as an add-on that runs on local tester agents.