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
Data Science and Machine Learning (Part 03): Matrix Regressions

Data Science and Machine Learning (Part 03): Matrix Regressions

This time our models are being made by matrices, which allows flexibility while it allows us to make powerful models that can handle not only five independent variables but also many variables as long as we stay within the calculations limits of a computer, this article is going to be an interesting read, that's for sure.
preview
Price Action Analysis Toolkit Development (Part 27): Liquidity Sweep With MA Filter Tool

Price Action Analysis Toolkit Development (Part 27): Liquidity Sweep With MA Filter Tool

Understanding the subtle dynamics behind price movements can give you a critical edge. One such phenomenon is the liquidity sweep, a deliberate strategy that large traders, especially institutions, use to push prices through key support or resistance levels. These levels often coincide with clusters of retail stop-loss orders, creating pockets of liquidity that big players can exploit to enter or exit sizeable positions with minimal slippage.
The market and the physics of its global patterns
The market and the physics of its global patterns

The market and the physics of its global patterns

In this article, I will try to test the assumption that any system with even a small understanding of the market can operate on a global scale. I will not invent any theories or patterns, but I will only use known facts, gradually translating these facts into the language of mathematical analysis.
Library for easy and quick development of MetaTrader programs (part VIII): Order and position modification events
Library for easy and quick development of MetaTrader programs (part VIII): Order and position modification events

Library for easy and quick development of MetaTrader programs (part VIII): 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 seventh part, we added tracking StopLimit orders activation and prepared the functionality for tracking other events involving orders and positions. In this article, we will develop the class for tracking order and position modification events.
preview
Trader-friendly stop loss and take profit

Trader-friendly stop loss and take profit

Stop loss and take profit can have a significant impact on trading results. In this article, we will look at several ways to find optimal stop order values.
Separate optimization of a strategy on trend and flat conditions
Separate optimization of a strategy on trend and flat conditions

Separate optimization of a strategy on trend and flat conditions

The article considers applying the separate optimization method during various market conditions. Separate optimization means defining trading system's optimal parameters by optimizing for an uptrend and downtrend separately. To reduce the effect of false signals and improve profitability, the systems are made flexible, meaning they have some specific set of settings or input data, which is justified because the market behavior is constantly changing.
preview
Neural networks made easy (Part 3): Convolutional networks

Neural networks made easy (Part 3): Convolutional networks

As a continuation of the neural network topic, I propose considering convolutional neural networks. This type of neural network are usually applied to analyzing visual imagery. In this article, we will consider the application of these networks in the financial markets.
preview
Python + MetaTrader 5: Fast Research Framework for Data, Features, and Prototypes

Python + MetaTrader 5: Fast Research Framework for Data, Features, and Prototypes

The article demonstrates how Python and MetaTrader 5 integration combines research flexibility and trade execution into a single workflow. Python is used for data analysis, feature selection and model training, while MetaTrader 5 is used for testing and trading automation. This approach simplifies the transfer of solutions into practice, increases reproducibility, and makes the development of trading systems faster and more structured.
Econometric Approach to Analysis of Charts
Econometric Approach to Analysis of Charts

Econometric Approach to Analysis of Charts

This article describes the econometric methods of analysis, the autocorrelation analysis and the analysis of conditional variance in particular. What is the benefit of the approach described here? Use of the non-linear GARCH models allows representing the analyzed series formally from the mathematical point of view and creating a forecast for a specified number of steps.
Combinatorics and probability for trading (Part IV): Bernoulli Logic
Combinatorics and probability for trading (Part IV): Bernoulli Logic

Combinatorics and probability for trading (Part IV): Bernoulli Logic

In this article, I decided to highlight the well-known Bernoulli scheme and to show how it can be used to describe trading-related data arrays. All this will then be used to create a self-adapting trading system. We will also look for a more generic algorithm, a special case of which is the Bernoulli formula, and will find an application for it.
preview
Brute force approach to pattern search

Brute force approach to pattern search

In this article, we will search for market patterns, create Expert Advisors based on the identified patterns, and check how long these patterns remain valid, if they ever retain their validity.
Combinatorics and probability theory for trading (Part II): Universal fractal
Combinatorics and probability theory for trading (Part II): Universal fractal

Combinatorics and probability theory for trading (Part II): Universal fractal

In this article, we will continue to study fractals and will pay special attention to summarizing all the material. To do this, I will try to bring all earlier developments into a compact form which would be convenient and understandable for practical application in trading.
Other classes in DoEasy library (Part 66): MQL5.com Signals collection class
Other classes in DoEasy library (Part 66): MQL5.com Signals collection class

Other classes in DoEasy library (Part 66): MQL5.com Signals collection class

In this article, I will create the signal collection class of the MQL5.com Signals service with the functions for managing signals. Besides, I will improve the Depth of Market snapshot object class for displaying the total DOM buy and sell volumes.
Controlling the Slope of Balance Curve During Work of an Expert Advisor
Controlling the Slope of Balance Curve During Work of an Expert Advisor

Controlling the Slope of Balance Curve During Work of an Expert Advisor

Finding rules for a trade system and programming them in an Expert Advisor is a half of the job. Somehow, you need to correct the operation of the Expert Advisor as it accumulates the results of trading. This article describes one of approaches, which allows improving performance of an Expert Advisor through creation of a feedback that measures slope of the balance curve.
Library for easy and quick development of MetaTrader programs (part III). Collection of market orders and positions, search and sorting
Library for easy and quick development of MetaTrader programs (part III). Collection of market orders and positions, search and sorting

Library for easy and quick development of MetaTrader programs (part III). Collection of market orders and positions, search and sorting

In the first part, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. Further on, we implemented the collection of history orders and deals. Our next step is creating a class for a convenient selection and sorting of orders, deals and positions in collection lists. We are going to implement the base library object called Engine and add collection of market orders and positions to the library.
Library for easy and quick development of MetaTrader programs (part XI). Compatibility with MQL4 - Position closure events
Library for easy and quick development of MetaTrader programs (part XI). Compatibility with MQL4 - Position closure events

Library for easy and quick development of MetaTrader programs (part XI). Compatibility with MQL4 - Position closure events

We continue the development of a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. In the tenth part, we resumed our work on the library compatibility with MQL4 and defined the events of opening positions and activating pending orders. In this article, we will define the events of closing positions and get rid of the unused order properties.
How to visualize multicurrency trading history based on HTML and CSV reports
How to visualize multicurrency trading history based on HTML and CSV reports

How to visualize multicurrency trading history based on HTML and CSV reports

Since its introduction, MetaTrader 5 provides multicurrency testing options. This possibility is often used by traders. However the function is not universal. The article presents several programs for drawing graphical objects on charts based on HTML and CSV trading history reports. Multicurrency trading can be analyzed in parallel, in several sub-windows, as well as in one window using the dynamic switching command.
preview
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.
preview
Neural networks made easy (Part 9): Documenting the work

Neural networks made easy (Part 9): Documenting the work

We have already passed a long way and the code in our library is becoming bigger and bigger. This makes it difficult to keep track of all connections and dependencies. Therefore, I suggest creating documentation for the earlier created code and to keep it updating with each new step. Properly prepared documentation will help us see the integrity of our work.
Self-organizing feature maps (Kohonen maps) - revisiting the subject
Self-organizing feature maps (Kohonen maps) - revisiting the subject

Self-organizing feature maps (Kohonen maps) - revisiting the subject

This article describes techniques of operating with Kohonen maps. The subject will be of interest to both market researchers with basic level of programing in MQL4 and MQL5 and experienced programmers that face difficulties with connecting Kohonen maps to their projects.
preview
Neural networks made easy (Part 26): Reinforcement Learning

Neural networks made easy (Part 26): Reinforcement Learning

We continue to study machine learning methods. With this article, we begin another big topic, Reinforcement Learning. This approach allows the models to set up certain strategies for solving the problems. We can expect that this property of reinforcement learning will open up new horizons for building trading strategies.
Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part II. Optimizing and forecasting
Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part II. Optimizing and forecasting

Practical Use of Kohonen Neural Networks in Algorithmic Trading. Part II. Optimizing and forecasting

Based on universal tools designed for working with Kohonen networks, we construct the system of analyzing and selecting the optimal EA parameters and consider forecasting time series. In Part I, we corrected and improved the publicly available neural network classes, having added necessary algorithms. Now, it is time to apply them to practice.
preview
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.
A scientific approach to the development of trading algorithms
A scientific approach to the development of trading algorithms

A scientific approach to the development of trading algorithms

The article considers the methodology for developing trading algorithms, in which a consistent scientific approach is used to analyze possible price patterns and to build trading algorithms based on these patterns. Development ideals are demonstrated using examples.
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.
Timeseries in DoEasy library (part 36): Object of timeseries for all used symbol periods
Timeseries in DoEasy library (part 36): Object of timeseries for all used symbol periods

Timeseries in DoEasy library (part 36): Object of timeseries for all used symbol periods

In this article, we will consider combining the lists of bar objects for each used symbol period into a single symbol timeseries object. Thus, each symbol will have an object storing the lists of all used symbol timeseries periods.
preview
Implementing an ARIMA training algorithm in MQL5

Implementing an ARIMA training algorithm in MQL5

In this article we will implement an algorithm that applies the Box and Jenkins Autoregressive Integrated Moving Average model by using Powells method of function minimization. Box and Jenkins stated that most time series could be modeled by one or both of two frameworks.
preview
Mastering Fair Value Gaps: Formation, Logic, and Automated Trading with Breakers and Market Structure Shifts

Mastering Fair Value Gaps: Formation, Logic, and Automated Trading with Breakers and Market Structure Shifts

This is an article that I have written aimed to expound and explain Fair Value Gaps, their formation logic for occurring, and automated trading with breakers and market structure shifts.
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.
preview
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.
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
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.
preview
Day Trading Larry Connors RSI2 Mean-Reversion Strategies

Day Trading Larry Connors RSI2 Mean-Reversion Strategies

Larry Connors is a renowned trader and author, best known for his work in quantitative trading and strategies like the 2-period RSI (RSI2), which helps identify short-term overbought and oversold market conditions. In this article, we’ll first explain the motivation behind our research, then recreate three of Connors’ most famous strategies in MQL5 and apply them to intraday trading of the S&P 500 index CFD.
preview
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.
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.
preview
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.