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
Combination scalping: analyzing trades from the past to increase the performance of future trades
Combination scalping: analyzing trades from the past to increase the performance of future trades

Combination scalping: analyzing trades from the past to increase the performance of future trades

The article provides the description of the technology aimed at increasing the effectiveness of any automated trading system. It provides a brief explanation of the idea, as well as its underlying basics, possibilities and disadvantages.
Library for easy and quick development of MetaTrader programs (part II). Collection of historical orders and deals
Library for easy and quick development of MetaTrader programs (part II). Collection of historical orders and deals

Library for easy and quick development of MetaTrader programs (part II). Collection of historical orders and deals

In the first part, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. We created the COrder abstract object which is a base object for storing data on history orders and deals, as well as on market orders and positions. Now we will develop all the necessary objects for storing account history data in collections.
Timeseries in DoEasy library (part 35): Bar object and symbol timeseries list
Timeseries in DoEasy library (part 35): Bar object and symbol timeseries list

Timeseries in DoEasy library (part 35): Bar object and symbol timeseries list

This article starts a new series about the creation of the DoEasy library for easy and fast program development. In the current article, we will implement the library functionality for accessing and working with symbol timeseries data. We are going to create the Bar object storing the main and extended timeseries bar data, and place bar objects to the timeseries list for convenient search and sorting of the objects.
Prices and Signals in DoEasy library (Part 65): Depth of Market collection and the class for working with MQL5.com Signals
Prices and Signals in DoEasy library (Part 65): Depth of Market collection and the class for working with MQL5.com Signals

Prices and Signals in DoEasy library (Part 65): Depth of Market collection and the class for working with MQL5.com Signals

In this article, I will create the collection class of Depths of Market of all symbols and start developing the functionality for working with the MQL5.com Signals service by creating the signal object class.
Neural Networks Cheap and Cheerful - Link NeuroPro with MetaTrader 5
Neural Networks Cheap and Cheerful - Link NeuroPro with MetaTrader 5

Neural Networks Cheap and Cheerful - Link NeuroPro with MetaTrader 5

If specific neural network programs for trading seem expensive and complex or, on the contrary, too simple, try NeuroPro. It is free and contains the optimal set of functionalities for amateurs. This article will tell you how to use it in conjunction with MetaTrader 5.
Sorting methods and their visualization using MQL5
Sorting methods and their visualization using MQL5

Sorting methods and their visualization using MQL5

The Graphic.mqh library has been designed to work with graphics in MQL5. The article provides an example of its practical application and explains the idea of sorting. The general concept of sorting is described here since each type of sorting already has at least one separate article, while some of sorting types are objects of detailed studies.
preview
Finding seasonal patterns in the forex market using the CatBoost algorithm

Finding seasonal patterns in the forex market using the CatBoost algorithm

The article considers the creation of machine learning models with time filters and discusses the effectiveness of this approach. The human factor can be eliminated now by simply instructing the model to trade at a certain hour of a certain day of the week. Pattern search can be provided by a separate algorithm.
Applying OLAP in trading (part 3): Analyzing quotes for the development of trading strategies
Applying OLAP in trading (part 3): Analyzing quotes for the development of trading strategies

Applying OLAP in trading (part 3): Analyzing quotes for the development of trading strategies

In this article we will continue dealing with the OLAP technology applied to trading. We will expand the functionality presented in the first two articles. This time we will consider the operational analysis of quotes. We will put forward and test the hypotheses on trading strategies based on aggregated historical data. The article presents Expert Advisors for studying bar patterns and adaptive trading.
preview
Neural networks made easy (Part 10): Multi-Head Attention

Neural networks made easy (Part 10): Multi-Head Attention

We have previously considered the mechanism of self-attention in neural networks. In practice, modern neural network architectures use several parallel self-attention threads to find various dependencies between the elements of a sequence. Let us consider the implementation of such an approach and evaluate its impact on the overall network performance.
Developing the symbol selection and navigation utility in MQL5 and MQL4
Developing the symbol selection and navigation utility in MQL5 and MQL4

Developing the symbol selection and navigation utility in MQL5 and MQL4

Experienced traders are well aware of the fact that most time-consuming things in trading are not opening and tracking positions but selecting symbols and looking for entry points. In this article, we will develop an EA simplifying the search for entry points on trading instruments provided by your broker.
preview
Risk and capital management using Expert Advisors

Risk and capital management using Expert Advisors

This article is about what you can not see in a backtest report, what you should expect using automated trading software, how to manage your money if you are using expert advisors, and how to cover a significant loss to remain in the trading activity when you are using automated procedures.
preview
Data Science and Machine Learning — Neural Network (Part 01): Feed Forward Neural Network demystified

Data Science and Machine Learning — Neural Network (Part 01): Feed Forward Neural Network demystified

Many people love them but a few understand the whole operations behind Neural Networks. In this article I will try to explain everything that goes behind closed doors of a feed-forward multi-layer perception in plain English.
Deep Neural Networks (Part II). Working out and selecting predictors
Deep Neural Networks (Part II). Working out and selecting predictors

Deep Neural Networks (Part II). Working out and selecting predictors

The second article of the series about deep neural networks will consider the transformation and choice of predictors during the process of preparing data for training a model.
Analysis of the Main Characteristics of Time Series
Analysis of the Main Characteristics of Time Series

Analysis of the Main Characteristics of Time Series

This article introduces a class designed to give a quick preliminary estimate of characteristics of various time series. As this takes place, statistical parameters and autocorrelation function are estimated, a spectral estimation of time series is carried out and a histogram is built.
Selection and navigation utility in MQL5 and MQL4: Adding auto search for patterns and displaying detected symbols
Selection and navigation utility in MQL5 and MQL4: Adding auto search for patterns and displaying detected symbols

Selection and navigation utility in MQL5 and MQL4: Adding auto search for patterns and displaying detected symbols

In this article, we continue expanding the features of the utility for collecting and navigating through symbols. This time, we will create new tabs displaying only the symbols that satisfy some of the necessary parameters and find out how to easily add custom tabs with the necessary sorting rules.
preview
An Analysis of Why Expert Advisors Fail

An Analysis of Why Expert Advisors Fail

This article presents an analysis of currency data to better understand why expert advisors can have good performance in some regions of time and poor performance in other regions of time.
Naive Bayes classifier for signals of a set of indicators
Naive Bayes classifier for signals of a set of indicators

Naive Bayes classifier for signals of a set of indicators

The article analyzes the application of the Bayes' formula for increasing the reliability of trading systems by means of using signals from multiple independent indicators. Theoretical calculations are verified with a simple universal EA, configured to work with arbitrary indicators.
preview
Modified Grid-Hedge EA in MQL5 (Part II): Making a Simple Grid EA

Modified Grid-Hedge EA in MQL5 (Part II): Making a Simple Grid EA

In this article, we explored the classic grid strategy, detailing its automation using an Expert Advisor in MQL5 and analyzing initial backtest results. We highlighted the strategy's need for high holding capacity and outlined plans for optimizing key parameters like distance, takeProfit, and lot sizes in future installments. The series aims to enhance trading strategy efficiency and adaptability to different market conditions.
Statistical Probability Distributions in MQL5
Statistical Probability Distributions in MQL5

Statistical Probability Distributions in MQL5

The article addresses probability distributions (normal, log-normal, binomial, logistic, exponential, Cauchy distribution, Student's t-distribution, Laplace distribution, Poisson distribution, Hyperbolic Secant distribution, Beta and Gamma distribution) of random variables used in Applied Statistics. It also features classes for handling these distributions.
preview
Data Science and Machine Learning — Neural Network (Part 02): Feed forward NN Architectures Design

Data Science and Machine Learning — Neural Network (Part 02): Feed forward NN Architectures Design

There are minor things to cover on the feed-forward neural network before we are through, the design being one of them. Let's see how we can build and design a flexible neural network to our inputs, the number of hidden layers, and the nodes for each of the network.
Social Trading. Can a profitable signal be made even better?
Social Trading. Can a profitable signal be made even better?

Social Trading. Can a profitable signal be made even better?

Most subscribers choose a trade signal by the beauty of the balance curve and by the number of subscribers. This is why many today's providers care of beautiful statistics rather than of real signal quality, often playing with lot sizes and artificially reducing the balance curve to an ideal appearance. This paper deals with the reliability criteria and the methods a provider may use to enhance its signal quality. An exemplary analysis of a specific signal history is presented, as well as methods that would help a provider to make it more profitable and less risky.
MQL Parsing by Means of MQL
MQL Parsing by Means of MQL

MQL Parsing by Means of MQL

The article describes a preprocessor, a scanner, and a parser to be used in parsing the MQL-based source codes. MQL implementation is attached.
preview
Neural networks made easy (Part 11): A take on GPT

Neural networks made easy (Part 11): A take on GPT

Perhaps one of the most advanced models among currently existing language neural networks is GPT-3, the maximal variant of which contains 175 billion parameters. Of course, we are not going to create such a monster on our home PCs. However, we can view which architectural solutions can be used in our work and how we can benefit from them.
preview
Decoding Opening Range Breakout Intraday Trading Strategies

Decoding Opening Range Breakout Intraday Trading Strategies

Opening Range Breakout (ORB) strategies are built on the idea that the initial trading range established shortly after the market opens reflects significant price levels where buyers and sellers agree on value. By identifying breakouts above or below a certain range, traders can capitalize on the momentum that often follows as the market direction becomes clearer. In this article, we will explore three ORB strategies adapted from the Concretum Group.
preview
How to build and optimize a cycle-based trading system (Detrended Price Oscillator - DPO)

How to build and optimize a cycle-based trading system (Detrended Price Oscillator - DPO)

This article explains how to design and optimise a trading system using the Detrended Price Oscillator (DPO) in MQL5. It outlines the indicator's core logic, demonstrating how it identifies short-term cycles by filtering out long-term trends. Through a series of step-by-step examples and simple strategies, readers will learn how to code it, define entry and exit signals, and conduct backtesting. Finally, the article presents practical optimization methods to enhance performance and adapt the system to changing market conditions.
Universal Regression Model for Market Price Prediction
Universal Regression Model for Market Price Prediction

Universal Regression Model for Market Price Prediction

The market price is formed out of a stable balance between demand and supply which, in turn, depend on a variety of economic, political and psychological factors. Differences in nature as well as causes of influence of these factors make it difficult to directly consider all the components. This article sets forth an attempt to predict the market price on the basis of an elaborated regression model.
Library for easy and quick development of MetaTrader programs (part XVI): Symbol collection events
Library for easy and quick development of MetaTrader programs (part XVI): Symbol collection events

Library for easy and quick development of MetaTrader programs (part XVI): Symbol collection events

In this article, we will create a new base class of all library objects adding the event functionality to all its descendants and develop the class for tracking symbol collection events based on the new base class. We will also change account and account event classes for developing the new base object functionality.
Statistical Carry Trade Strategy
Statistical Carry Trade Strategy

Statistical Carry Trade Strategy

An algorithm of statistical protection of open positive swap positions from unwanted price movements. This article features a variant of the carry trade protection strategy that allows to compensate for potential risk of the price movement in the direction opposite to that of the open position.
Applying OLAP in trading (part 2): Visualizing the interactive multidimensional data analysis results
Applying OLAP in trading (part 2): Visualizing the interactive multidimensional data analysis results

Applying OLAP in trading (part 2): Visualizing the interactive multidimensional data analysis results

In this article, we consider the creation of an interactive graphical interface for an MQL program, which is designed for the processing of account history and trading reports using OLAP techniques. To obtain a visual result, we will use maximizable and scalable windows, an adaptive layout of rubber controls and a new control for displaying diagrams. To provide the visualization functionality, we will implement a GUI with the selection of variables along coordinate axes, as well as with the selection of aggregate functions, diagram types and sorting options.
Risk Evaluation in the Sequence of Deals with One Asset
Risk Evaluation in the Sequence of Deals with One Asset

Risk Evaluation in the Sequence of Deals with One Asset

This article describes the use of methods of the theory of probability and mathematical statistics in the analysis of trading systems.
Visualizing trading strategy optimization in MetaTrader 5
Visualizing trading strategy optimization in MetaTrader 5

Visualizing trading strategy optimization in MetaTrader 5

The article implements an MQL application with a graphical interface for extended visualization of the optimization process. The graphical interface applies the last version of EasyAndFast library. Many users may ask why they need graphical interfaces in MQL applications. This article demonstrates one of multiple cases where they can be useful for traders.
Library for easy and quick development of MetaTrader programs (part XII): Account object class and collection of account objects
Library for easy and quick development of MetaTrader programs (part XII): Account object class and collection of account objects

Library for easy and quick development of MetaTrader programs (part XII): Account object class and collection of account objects

In the previous article, we defined position closure events for MQL4 in the library and got rid of the unused order properties. Here we will consider the creation of the Account object, develop the collection of account objects and prepare the functionality for tracking account events.
Combinatorics and probability theory for trading (Part III): The first mathematical model
Combinatorics and probability theory for trading (Part III): The first mathematical model

Combinatorics and probability theory for trading (Part III): The first mathematical model

A logical continuation of the earlier discussed topic would be the development of multifunctional mathematical models for trading tasks. In this article, I will describe the entire process related to the development of the first mathematical model describing fractals, from scratch. This model should become an important building block and be multifunctional and universal. It will build up our theoretical basis for further development of this idea.
preview
Neural networks made easy (Part 8): Attention mechanisms

Neural networks made easy (Part 8): Attention mechanisms

In previous articles, we have already tested various options for organizing neural networks. We also considered convolutional networks borrowed from image processing algorithms. In this article, I suggest considering Attention Mechanisms, the appearance of which gave impetus to the development of language models.
Library for easy and quick development of MetaTrader programs (part X): Compatibility with MQL4 - Events of opening a position and activating pending orders
Library for easy and quick development of MetaTrader programs (part X): Compatibility with MQL4 - Events of opening a position and activating pending orders

Library for easy and quick development of MetaTrader programs (part X): Compatibility with MQL4 - Events of opening a position and activating pending orders

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 ninth part, we started improving the library classes for working with MQL4. Here we will continue improving the library to ensure its full compatibility with MQL4.
preview
Automating Trading Strategies in MQL5 (Part 43): Adaptive Linear Regression Channel Strategy

Automating Trading Strategies in MQL5 (Part 43): Adaptive Linear Regression Channel Strategy

In this article, we implement an adaptive Linear Regression Channel system in MQL5 that automatically calculates the regression line and standard deviation channel over a user-defined period, only activates when the slope exceeds a minimum threshold to confirm a clear trend, and dynamically recreates or extends the channel when the price breaks out by a configurable percentage of channel width.
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.
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 53): Pattern Density Heatmap for Support and Resistance Zone Discovery

Price Action Analysis Toolkit Development (Part 53): Pattern Density Heatmap for Support and Resistance Zone Discovery

This article introduces the Pattern Density Heatmap, a price‑action mapping tool that transforms repeated candlestick pattern detections into statistically significant support and resistance zones. Rather than treating each signal in isolation, the EA aggregates detections into fixed price bins, scores their density with optional recency weighting, and confirms levels against higher‑timeframe data. The resulting heatmap reveals where the market has historically reacted—levels that can be used proactively for trade timing, risk management, and strategy confidence across any trading style.
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.