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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Matrix and Vector operations in MQL5

Matrix and Vector operations in MQL5

Matrices and vectors have been introduced in MQL5 for efficient operations with mathematical solutions. The new types offer built-in methods for creating concise and understandable code that is close to mathematical notation. Arrays provide extensive capabilities, but there are many cases in which matrices are much more efficient.
Movement continuation model - searching on the chart and execution statistics
Movement continuation model - searching on the chart and execution statistics

Movement continuation model - searching on the chart and execution statistics

This article provides programmatic definition of one of the movement continuation models. The main idea is defining two waves — the main and the correction one. For extreme points, I apply fractals as well as "potential" fractals - extreme points that have not yet formed as fractals.
Prices in DoEasy library (Part 64): Depth of Market, classes of DOM snapshot and snapshot series objects
Prices in DoEasy library (Part 64): Depth of Market, classes of DOM snapshot and snapshot series objects

Prices in DoEasy library (Part 64): Depth of Market, classes of DOM snapshot and snapshot series objects

In this article, I will create two classes (the class of DOM snapshot object and the class of DOM snapshot series object) and test creation of the DOM data series.
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Combinatorics and probability for trading (Part V): Curve analysis

Combinatorics and probability for trading (Part V): Curve analysis

In this article, I decided to conduct a study related to the possibility of reducing multiple states to double-state systems. The main purpose of the article is to analyze and to come to useful conclusions that may help in the further development of scalable trading algorithms based on the probability theory. Of course, this topic involves mathematics. However, given the experience of previous articles, I see that generalized information is more useful than details.
Deep Neural Networks (Part III). Sample selection and dimensionality reduction
Deep Neural Networks (Part III). Sample selection and dimensionality reduction

Deep Neural Networks (Part III). Sample selection and dimensionality reduction

This article is a continuation of the series of articles about deep neural networks. Here we will consider selecting samples (removing noise), reducing the dimensionality of input data and dividing the data set into the train/val/test sets during data preparation for training the neural network.
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Brute force approach to pattern search (Part III): New horizons

Brute force approach to pattern search (Part III): New horizons

This article provides a continuation to the brute force topic, and it introduces new opportunities for market analysis into the program algorithm, thereby accelerating the speed of analysis and improving the quality of results. New additions enable the highest-quality view of global patterns within this approach.
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Neural networks made easy (Part 5): Multithreaded calculations in OpenCL

Neural networks made easy (Part 5): Multithreaded calculations in OpenCL

We have earlier discussed some types of neural network implementations. In the considered networks, the same operations are repeated for each neuron. A logical further step is to utilize multithreaded computing capabilities provided by modern technology in an effort to speed up the neural network learning process. One of the possible implementations is described in this article.
Checking the Myth: The Whole Day Trading Depends on How the Asian Session Is Traded
Checking the Myth: The Whole Day Trading Depends on How the Asian Session Is Traded

Checking the Myth: The Whole Day Trading Depends on How the Asian Session Is Traded

In this article we will check the well-known statement that "The whole day trading depends on how the Asian session is traded".
Optimal approach to the development and analysis of trading systems
Optimal approach to the development and analysis of trading systems

Optimal approach to the development and analysis of trading systems

In this article, I will show the criteria to be used when selecting a system or a signal for investing your funds, as well as describe the optimal approach to the development of trading systems and highlight the importance of this matter in Forex trading.
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Neural networks made easy (Part 27): Deep Q-Learning (DQN)

Neural networks made easy (Part 27): Deep Q-Learning (DQN)

We continue to study reinforcement learning. In this article, we will get acquainted with the Deep Q-Learning method. The use of this method has enabled the DeepMind team to create a model that can outperform a human when playing Atari computer games. I think it will be useful to evaluate the possibilities of the technology for solving trading problems.
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Price Action Analysis Toolkit Development (Part 32): Python Candlestick Recognition Engine (II) — Detection Using Ta-Lib

Price Action Analysis Toolkit Development (Part 32): Python Candlestick Recognition Engine (II) — Detection Using Ta-Lib

In this article, we’ve transitioned from manually coding candlestick‑pattern detection in Python to leveraging TA‑Lib, a library that recognizes over sixty distinct patterns. These formations offer valuable insights into potential market reversals and trend continuations. Follow along to learn more.
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Algorithmic Trading With MetaTrader 5 And R For Beginners

Algorithmic Trading With MetaTrader 5 And R For Beginners

Embark on a compelling exploration where financial analysis meets algorithmic trading as we unravel the art of seamlessly uniting R and MetaTrader 5. This article is your guide to bridging the realms of analytical finesse in R with the formidable trading capabilities of MetaTrader 5.
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Price Action Analysis Toolkit Development (Part 51): Revolutionary Chart Search Technology for Candlestick Pattern Discovery

Price Action Analysis Toolkit Development (Part 51): Revolutionary Chart Search Technology for Candlestick Pattern Discovery

This article is intended for algorithmic traders, quantitative analysts, and MQL5 developers interested in enhancing their understanding of candlestick pattern recognition through practical implementation. It provides an in‑depth exploration of the CandlePatternSearch.mq5 Expert Advisor—a complete framework for detecting, visualizing, and monitoring classical candlestick formations in MetaTrader 5. Beyond a line‑by‑line review of the code, the article discusses architectural design, pattern detection logic, GUI integration, and alert mechanisms, illustrating how traditional price‑action analysis can be automated efficiently.
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Understand and Use MQL5 Strategy Tester Effectively

Understand and Use MQL5 Strategy Tester Effectively

There is an essential need for MQL5 programmers or developers to master important and valuable tools. One of these tools is the Strategy Tester, this article is a practical guide to understanding and using the strategy tester of MQL5.
Regression Analysis of the Influence of Macroeconomic Data on Currency Prices Fluctuation
Regression Analysis of the Influence of Macroeconomic Data on Currency Prices Fluctuation

Regression Analysis of the Influence of Macroeconomic Data on Currency Prices Fluctuation

This article considers the application of multiple regression analysis to macroeconomic statistics. It also gives an insight into the evaluation of the statistics impact on the currency exchange rate fluctuation based on the example of the currency pair EURUSD. Such evaluation allows automating the fundamental analysis which becomes available to even novice traders.
Multiple Null Bar Re-Count in Some Indicators
Multiple Null Bar Re-Count in Some Indicators

Multiple Null Bar Re-Count in Some Indicators

The article is concerned with the problem of re-counting of the indicator value in the MetaTrader 4 Client Terminal when the null bar changes. It outlines general idea of how to add to the indicator code some extra program items that allow to restore program code saved before multiple re-counting.
Other classes in DoEasy library (Part 72): Tracking and recording chart object parameters in the collection
Other classes in DoEasy library (Part 72): Tracking and recording chart object parameters in the collection

Other classes in DoEasy library (Part 72): Tracking and recording chart object parameters in the collection

In this article, I will complete working with chart object classes and their collection. I will also implement auto tracking of changes in chart properties and their windows, as well as saving new parameters to the object properties. Such a revision allows the future implementation of an event functionality for the entire chart collection.
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Neural networks made easy (Part 6): Experimenting with the neural network learning rate

Neural networks made easy (Part 6): Experimenting with the neural network learning rate

We have previously considered various types of neural networks along with their implementations. In all cases, the neural networks were trained using the gradient decent method, for which we need to choose a learning rate. In this article, I want to show the importance of a correctly selected rate and its impact on the neural network training, using examples.
Library for easy and quick development of MetaTrader programs (part VII): StopLimit order activation events, preparing the functionality for order and position modification events
Library for easy and quick development of MetaTrader programs (part VII): StopLimit order activation events, preparing the functionality for order and position modification events

Library for easy and quick development of MetaTrader programs (part VII): StopLimit order activation events, preparing the functionality for order and position modification events

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 sixth part, we trained the library to work with positions on netting accounts. Here we will implement tracking StopLimit orders activation and prepare the functionality to track order and position modification events.
Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part I. Tools
Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part I. Tools

Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part I. Tools

The present article develops the idea of using Kohonen Maps in MetaTrader 5, covered in some previous publications. The improved and enhanced classes provide tools to solve application tasks.
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Price Action Analysis Toolkit Development (Part 1): Chart Projector

Price Action Analysis Toolkit Development (Part 1): Chart Projector

This project aims to leverage the MQL5 algorithm to develop a comprehensive set of analysis tools for MetaTrader 5. These tools—ranging from scripts and indicators to AI models and expert advisors—will automate the market analysis process. At times, this development will yield tools capable of performing advanced analyses with no human involvement and forecasting outcomes to appropriate platforms. No opportunity will ever be missed. Join me as we explore the process of building a robust market analysis custom tools' chest. We will begin by developing a simple MQL5 program that I have named, Chart Projector.
Prices in DoEasy library (part 63): Depth of Market and its abstract request class
Prices in DoEasy library (part 63): Depth of Market and its abstract request class

Prices in DoEasy library (part 63): Depth of Market and its abstract request class

In the article, I will start developing the functionality for working with the Depth of Market. I will also create the class of the Depth of Market abstract order object and its descendants.
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Multi-module trading robot in Python and MQL5 (Part I): Creating basic architecture and first modules

Multi-module trading robot in Python and MQL5 (Part I): Creating basic architecture and first modules

We are going to develop a modular trading system that combines Python for data analysis with MQL5 for trade execution. Four independent modules monitor different market aspects in parallel: volumes, arbitrage, economics and risks, and use RandomForest with 400 trees for analysis. Particular emphasis is placed on risk management, since even the most advanced trading algorithms are useless without proper risk management.
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Price Action Analysis Toolkit Development (Part 3): Analytics Master — EA

Price Action Analysis Toolkit Development (Part 3): Analytics Master — EA

Moving from a simple trading script to a fully functioning Expert Advisor (EA) can significantly enhance your trading experience. Imagine having a system that automatically monitors your charts, performs essential calculations in the background, and provides regular updates every two hours. This EA would be equipped to analyze key metrics that are crucial for making informed trading decisions, ensuring that you have access to the most current information to adjust your strategies effectively.
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Price Action Analysis Toolkit Development (Part 25): Dual EMA Fractal Breaker

Price Action Analysis Toolkit Development (Part 25): Dual EMA Fractal Breaker

Price action is a fundamental approach for identifying profitable trading setups. However, manually monitoring price movements and patterns can be challenging and time-consuming. To address this, we are developing tools that analyze price action automatically, providing timely signals whenever potential opportunities are detected. This article introduces a robust tool that leverages fractal breakouts alongside EMA 14 and EMA 200 to generate reliable trading signals, helping traders make informed decisions with greater confidence.
Timeseries in DoEasy library (part 46): Multi-period multi-symbol indicator buffers
Timeseries in DoEasy library (part 46): Multi-period multi-symbol indicator buffers

Timeseries in DoEasy library (part 46): Multi-period multi-symbol indicator buffers

In this article, I am going to improve the classes of indicator buffer objects to work in the multi-symbol mode. This will pave the way for creating multi-symbol multi-period indicators in custom programs. I will add the missing functionality to the calculated buffer objects allowing us to create multi-symbol multi-period standard indicators.
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Data Science and Machine Learning (Part 09): The K-Nearest Neighbors Algorithm (KNN)

Data Science and Machine Learning (Part 09): The K-Nearest Neighbors Algorithm (KNN)

This is a lazy algorithm that doesn't learn from the training dataset, it stores the dataset instead and acts immediately when it's given a new sample. As simple as it is, it is used in a variety of real-world applications.
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Data Science and Machine Learning (Part 11): Naïve Bayes, Probability theory in Trading

Data Science and Machine Learning (Part 11): Naïve Bayes, Probability theory in Trading

Trading with probability is like walking on a tightrope - it requires precision, balance, and a keen understanding of risk. In the world of trading, the probability is everything. It's the difference between success and failure, profit and loss. By leveraging the power of probability, traders can make informed decisions, manage risk effectively, and achieve their financial goals. So, whether you're a seasoned investor or a novice trader, understanding probability is the key to unlocking your trading potential. In this article, we'll explore the exciting world of trading with probability and show you how to take your trading game to the next level.
MetaTrader AppStore Results for Q3 2013
MetaTrader AppStore Results for Q3 2013

MetaTrader AppStore Results for Q3 2013

Another quarter of the year has passed and we have decided to sum up its results for MetaTrader AppStore - the largest store of trading robots and technical indicators for MetaTrader platforms. More than 500 developers have placed over 1 200 products in the Market by the end of the reported quarter.
Price series discretization, random component and noise
Price series discretization, random component and noise

Price series discretization, random component and noise

We usually analyze the market using candlesticks or bars that slice the price series into regular intervals. Doesn't such discretization method distort the real structure of market movements? Discretization of an audio signal at regular intervals is an acceptable solution because an audio signal is a function that changes over time. The signal itself is an amplitude which depends on time. This signal property is fundamental.
Timeseries in DoEasy library (part 45): Multi-period indicator buffers
Timeseries in DoEasy library (part 45): Multi-period indicator buffers

Timeseries in DoEasy library (part 45): Multi-period indicator buffers

In this article, I will start the improvement of the indicator buffer objects and collection class for working in multi-period and multi-symbol modes. I am going to consider the operation of buffer objects for receiving and displaying data from any timeframe on the current symbol chart.
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Algorithmic trading based on 3D reversal patterns

Algorithmic trading based on 3D reversal patterns

Discovering a new world of automated trading on 3D bars. What does a trading robot look like on multidimensional price bars? Are "yellow" clusters of 3D bars able to predict trend reversals? What does multidimensional trading look like?
Building a Spectrum Analyzer
Building a Spectrum Analyzer

Building a Spectrum Analyzer

This article is intended to get its readers acquainted with a possible variant of using graphical objects of the MQL5 language. It analyses an indicator, which implements a panel of managing a simple spectrum analyzer using the graphical objects. The article is meant for readers acquianted with basics of MQL5.
Library for easy and quick development of MetaTrader programs (part VI): Netting account events
Library for easy and quick development of MetaTrader programs (part VI): Netting account events

Library for easy and quick development of MetaTrader programs (part VI): Netting account events

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 fifth part of the article series, we created trading event classes and the event collection, from which the events are sent to the base object of the Engine library and the control program chart. In this part, we will let the library to work on netting accounts.
Statistical Estimations
Statistical Estimations

Statistical Estimations

Estimation of statistical parameters of a sequence is very important, since most of mathematical models and methods are based on different assumptions. For example, normality of distribution law or dispersion value, or other parameters. Thus, when analyzing and forecasting of time series we need a simple and convenient tool that allows quickly and clearly estimating the main statistical parameters. The article shortly describes the simplest statistical parameters of a random sequence and several methods of its visual analysis. It offers the implementation of these methods in MQL5 and the methods of visualization of the result of calculations using the Gnuplot application.
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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.
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Developing a Replay System — Market simulation (Part 01): First experiments (I)

Developing a Replay System — Market simulation (Part 01): First experiments (I)

How about creating a system that would allow us to study the market when it is closed or even to simulate market situations? Here we are going to start a new series of articles in which we will deal with this topic.
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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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Data Science and Machine Learning (Part 04): Predicting Current Stock Market Crash

Data Science and Machine Learning (Part 04): Predicting Current Stock Market Crash

In this article I am going to attempt to use our logistic model to predict the stock market crash based upon the fundamentals of the US economy, the NETFLIX and APPLE are the stocks we are going to focus on, Using the previous market crashes of 2019 and 2020 let's see how our model will perform in the current dooms and glooms.
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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.