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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Brute force approach to pattern search (Part II): Immersion

Brute force approach to pattern search (Part II): Immersion

In this article we will continue discussing the brute force approach. I will try to provide a better explanation of the pattern using the new improved version of my application. I will also try to find the difference in stability using different time intervals and timeframes.
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MQL5 Wizard techniques you should know (Part 01): Regression Analysis

MQL5 Wizard techniques you should know (Part 01): Regression Analysis

Todays trader is a philomath who is almost always (either consciously or not...) looking up new ideas, trying them out, choosing to modify them or discard them; an exploratory process that should cost a fair amount of diligence. This clearly places a premium on the trader's time and the need to avoid mistakes. These series of articles will proposition that the MQL5 wizard should be a mainstay for traders. Why? Because not only does the trader save time by assembling his new ideas with the MQL5 wizard, and greatly reduce mistakes from duplicate coding; he is ultimately set-up to channel his energy on the few critical areas of his trading philosophy.
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Price Action Analysis Toolkit Development (Part 6): Mean Reversion Signal Reaper

Price Action Analysis Toolkit Development (Part 6): Mean Reversion Signal Reaper

While some concepts may seem straightforward at first glance, bringing them to life in practice can be quite challenging. In the article below, we'll take you on a journey through our innovative approach to automating an Expert Advisor (EA) that skillfully analyzes the market using a mean reversion strategy. Join us as we unravel the intricacies of this exciting automation process.
Other classes in DoEasy library (Part 70): Expanding functionality and auto updating the chart object collection
Other classes in DoEasy library (Part 70): Expanding functionality and auto updating the chart object collection

Other classes in DoEasy library (Part 70): Expanding functionality and auto updating the chart object collection

In this article, I will expand the functionality of chart objects and arrange navigation through charts, creation of screenshots, as well as saving and applying templates to charts. Also, I will implement auto update of the collection of chart objects, their windows and indicators within them.
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Population optimization algorithms: Particle swarm (PSO)

Population optimization algorithms: Particle swarm (PSO)

In this article, I will consider the popular Particle Swarm Optimization (PSO) algorithm. Previously, we discussed such important characteristics of optimization algorithms as convergence, convergence rate, stability, scalability, as well as developed a test stand and considered the simplest RNG algorithm.
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Visual evaluation of optimization results

Visual evaluation of optimization results

In this article, we will consider how to build graphs of all optimization passes and to select the optimal custom criterion. We will also see how to create a desired solution with little MQL5 knowledge, using the articles published on the website and forum comments.
Filtering Signals Based on Statistical Data of Price Correlation
Filtering Signals Based on Statistical Data of Price Correlation

Filtering Signals Based on Statistical Data of Price Correlation

Is there any correlation between the past price behavior and its future trends? Why does the price repeat today the character of its previous day movement? Can the statistics be used to forecast the price dynamics? There is an answer, and it is positive. If you have any doubt, then this article is for you. I'll tell how to create a working filter for a trading system in MQL5, revealing an interesting pattern in price changes.
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MQL5 Wizard techniques you should know (Part 05): Markov Chains

MQL5 Wizard techniques you should know (Part 05): Markov Chains

Markov chains are a powerful mathematical tool that can be used to model and forecast time series data in various fields, including finance. In financial time series modelling and forecasting, Markov chains are often used to model the evolution of financial assets over time, such as stock prices or exchange rates. One of the main advantages of Markov chain models is their simplicity and ease of use.
Library for easy and quick development of MetaTrader programs (part IX): Compatibility with MQL4 - Preparing data
Library for easy and quick development of MetaTrader programs (part IX): Compatibility with MQL4 - Preparing data

Library for easy and quick development of MetaTrader programs (part IX): Compatibility with MQL4 - Preparing data

In the previous articles, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. In the eighth part, we implemented the class for tracking order and position modification events. Here, we will improve the library by making it fully compatible with MQL4.
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Regression models of the Scikit-learn Library and their export to ONNX

Regression models of the Scikit-learn Library and their export to ONNX

In this article, we will explore the application of regression models from the Scikit-learn package, attempt to convert them into ONNX format, and use the resultant models within MQL5 programs. Additionally, we will compare the accuracy of the original models with their ONNX versions for both float and double precision. Furthermore, we will examine the ONNX representation of regression models, aiming to provide a better understanding of their internal structure and operational principles.
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Building a Trading System (Part 2): The Science of Position Sizing

Building a Trading System (Part 2): The Science of Position Sizing

Even with a positive-expectancy system, position sizing determines whether you thrive or collapse. It’s the pivot of risk management—translating statistical edges into real-world results while safeguarding your capital.
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MQL5 Wizard techniques you should know (Part 06): Fourier Transform

MQL5 Wizard techniques you should know (Part 06): Fourier Transform

The Fourier transform introduced by Joseph Fourier is a means of deconstructing complex data wave points into simple constituent waves. This feature could be resourceful to traders and this article takes a look at that.
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Gradient boosting in transductive and active machine learning

Gradient boosting in transductive and active machine learning

In this article, we will consider active machine learning methods utilizing real data, as well discuss their pros and cons. Perhaps you will find these methods useful and will include them in your arsenal of machine learning models. Transduction was introduced by Vladimir Vapnik, who is the co-inventor of the Support-Vector Machine (SVM).
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Price Action Analysis Toolkit Development (Part 38): Tick Buffer VWAP and Short-Window Imbalance Engine

Price Action Analysis Toolkit Development (Part 38): Tick Buffer VWAP and Short-Window Imbalance Engine

In Part 38, we build a production-grade MT5 monitoring panel that converts raw ticks into actionable signals. The EA buffers tick data to compute tick-level VWAP, a short-window imbalance (flow) metric, and ATR-based position sizing. It then visualizes spread, ATR, and flow with low-flicker bars. The system calculates a suggested lot size and a 1R stop, and issues configurable alerts for tight spreads, strong flow, and edge conditions. Auto-trading is intentionally disabled; the focus remains on robust signal generation and a clean user experience.
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Developing a trading robot in Python (Part 3): Implementing a model-based trading algorithm

Developing a trading robot in Python (Part 3): Implementing a model-based trading algorithm

We continue the series of articles on developing a trading robot in Python and MQL5. In this article, we will create a trading algorithm in Python.
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Neural networks made easy (Part 14): Data clustering

Neural networks made easy (Part 14): Data clustering

It has been more than a year since I published my last article. This is quite a lot time to revise ideas and to develop new approaches. In the new article, I would like to divert from the previously used supervised learning method. This time we will dip into unsupervised learning algorithms. In particular, we will consider one of the clustering algorithms—k-means.
Prices in DoEasy library (part 60): Series list of symbol tick data
Prices in DoEasy library (part 60): Series list of symbol tick data

Prices in DoEasy library (part 60): Series list of symbol tick data

In this article, I will create the list for storing tick data of a single symbol and check its creation and retrieval of required data in an EA. Tick data lists that are individual for each used symbol will further constitute a collection of tick data.
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Alan Andrews and his methods of time series analysis

Alan Andrews and his methods of time series analysis

Alan Andrews is one of the most famous "educators" of the modern world in the field of trading. His "pitchfork" is included in almost all modern quote analysis programs. But most traders do not use even a fraction of the opportunities that this tool provides. Besides, Andrews' original training course includes a description not only of the pitchfork (although it remains the main tool), but also of some other useful constructions. The article provides an insight into the marvelous chart analysis methods that Andrews taught in his original course. Beware, there will be a lot of images.
Calculation of Integral Characteristics of Indicator Emissions
Calculation of Integral Characteristics of Indicator Emissions

Calculation of Integral Characteristics of Indicator Emissions

Indicator emissions are a little-studied area of market research. Primarily, this is due to the difficulty of analysis that is caused by the processing of very large arrays of time-varying data. Existing graphical analysis is too resource intensive and has therefore triggered the development of a parsimonious algorithm that uses time series of emissions. This article demonstrates how visual (intuitive image) analysis can be replaced with the study of integral characteristics of emissions. It can be of interest to both traders and developers of automated trading systems.
Jeremy Scott - Successful MQL5 Market Seller
Jeremy Scott - Successful MQL5 Market Seller

Jeremy Scott - Successful MQL5 Market Seller

Jeremy Scott who is better known under Johnnypasado nickname at MQL5.community became famous offering products in our MQL5 Market service. Jeremy has already made several thousands of dollars in the Market and that is not the limit. We decided to take a closer look at the future millionaire and receive some pieces of advice for MQL5 Market sellers.
Prices in DoEasy library (part 62): Updating tick series in real time, preparation for working with Depth of Market
Prices in DoEasy library (part 62): Updating tick series in real time, preparation for working with Depth of Market

Prices in DoEasy library (part 62): Updating tick series in real time, preparation for working with Depth of Market

In this article, I will implement updating tick data in real time and prepare the symbol object class for working with Depth of Market (DOM itself is to be implemented in the next article).
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Timeseries in DoEasy library (part 58): Timeseries of indicator buffer data

Timeseries in DoEasy library (part 58): Timeseries of indicator buffer data

In conclusion of the topic of working with timeseries organise storage, search and sort of data stored in indicator buffers which will allow to further perform the analysis based on values of the indicators to be created on the library basis in programs. The general concept of all collection classes of the library allows to easily find necessary data in the corresponding collection. Respectively, the same will be possible in the class created today.
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Developing a Replay System — Market simulation (Part 03): Adjusting the settings (I)

Developing a Replay System — Market simulation (Part 03): Adjusting the settings (I)

Let's start by clarifying the current situation, because we didn't start in the best way. If we don't do it now, we'll be in trouble soon.
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Automating Trading Strategies with Parabolic SAR Trend Strategy in MQL5: Crafting an Effective Expert Advisor

Automating Trading Strategies with Parabolic SAR Trend Strategy in MQL5: Crafting an Effective Expert Advisor

In this article, we will automate the trading strategies with Parabolic SAR Strategy in MQL5: Crafting an Effective Expert Advisor. The EA will make trades based on trends identified by the Parabolic SAR indicator.
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Rebuy algorithm: Math model for increasing efficiency

Rebuy algorithm: Math model for increasing efficiency

In this article, we will use the rebuy algorithm for a deeper understanding of the efficiency of trading systems and start working on the general principles of improving trading efficiency using mathematics and logic, as well as apply the most non-standard methods of increasing efficiency in terms of using absolutely any trading system.
How to create and test custom MOEX symbols in MetaTrader 5
How to create and test custom MOEX symbols in MetaTrader 5

How to create and test custom MOEX symbols in MetaTrader 5

The article describes the creation of a custom exchange symbol using the MQL5 language. In particular, it considers the use of exchange quotes from the popular Finam website. Another option considered in this article is the possibility to work with an arbitrary format of text files used in the creation of the custom symbol. This allows working with any financial symbols and data sources. After creating a custom symbol, we can use all the capabilities of the MetaTrader 5 Strategy Tester to test trading algorithms for exchange instruments.
The Role of Statistical Distributions in Trader's Work
The Role of Statistical Distributions in Trader's Work

The Role of Statistical Distributions in Trader's Work

This article is a logical continuation of my article Statistical Probability Distributions in MQL5 which set forth the classes for working with some theoretical statistical distributions. Now that we have a theoretical base, I suggest that we should directly proceed to real data sets and try to make some informational use of this base.
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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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MetaTrader 5 Machine Learning Blueprint (Part 2): Labeling Financial Data for Machine Learning

MetaTrader 5 Machine Learning Blueprint (Part 2): Labeling Financial Data for Machine Learning

In this second installment of the MetaTrader 5 Machine Learning Blueprint series, you’ll discover why simple labels can lead your models astray—and how to apply advanced techniques like the Triple-Barrier and Trend-Scanning methods to define robust, risk-aware targets. Packed with practical Python examples that optimize these computationally intensive techniques, this hands-on guide shows you how to transform noisy market data into reliable labels that mirror real-world trading conditions.
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Data Science and Machine Learning (Part 10): Ridge Regression

Data Science and Machine Learning (Part 10): Ridge Regression

Ridge regression is a simple technique to reduce model complexity and prevent over-fitting which may result from simple linear regression
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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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Monte Carlo Permutation Tests in MetaTrader 5

Monte Carlo Permutation Tests in MetaTrader 5

In this article we take a look at how we can conduct permutation tests based on shuffled tick data on any expert advisor using only Metatrader 5.
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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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Creating volatility forecast indicator using Python

Creating volatility forecast indicator using Python

In this article, we will forecast future extreme volatility using binary classification. Besides, we will develop an extreme volatility forecast indicator using machine learning.
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Price Action Analysis Toolkit Development (Part 47): Tracking Forex Sessions and Breakouts in MetaTrader 5

Price Action Analysis Toolkit Development (Part 47): Tracking Forex Sessions and Breakouts in MetaTrader 5

Global market sessions shape the rhythm of the trading day, and understanding their overlap is vital to timing entries and exits. In this article, we’ll build an interactive trading sessions  EA that brings those global hours to life directly on your chart. The EA automatically plots color‑coded rectangles for the Asia, Tokyo, London, and New York sessions, updating in real time as each market opens or closes. It features on‑chart toggle buttons, a dynamic information panel, and a scrolling ticker headline that streams live status and breakout messages. Tested on different brokers, this EA combines precision with style—helping traders see volatility transitions, identify cross‑session breakouts, and stay visually connected to the global market’s pulse.
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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.
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Price Action Analysis Toolkit Development (Part 52): Master Market Structure with Multi-Timeframe Visual Analysis

Price Action Analysis Toolkit Development (Part 52): Master Market Structure with Multi-Timeframe Visual Analysis

This article presents the Multi‑Timeframe Visual Analyzer, an MQL5 Expert Advisor that reconstructs and overlays higher‑timeframe candles directly onto your active chart. It explains the implementation, key inputs, and practical outcomes, supported by an animated demo and chart examples showing instant toggling, multi‑timeframe confirmation, and configurable alerts. Read on to see how this tool can make chart analysis faster, clearer, and more efficient.
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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Integration of Broker APIs with Expert Advisors using MQL5 and Python

Integration of Broker APIs with Expert Advisors using MQL5 and Python

In this article, we will discuss the implementation of MQL5 in partnership with Python to perform broker-related operations. Imagine having a continuously running Expert Advisor (EA) hosted on a VPS, executing trades on your behalf. At some point, the ability of the EA to manage funds becomes paramount. This includes operations such as topping up your trading account and initiating withdrawals. In this discussion, we will shed light on the advantages and practical implementation of these features, ensuring seamless integration of fund management into your trading strategy. Stay tuned!
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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.