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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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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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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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.
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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).
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 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.
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.
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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.
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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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.
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.
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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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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.
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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Creating a mean-reversion strategy based on machine learning

Creating a mean-reversion strategy based on machine learning

This article proposes another original approach to creating trading systems based on machine learning, using clustering and trade labeling for mean reversion strategies.
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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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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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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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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 26): Pin Bar, Engulfing Patterns and RSI Divergence (Multi-Pattern) Tool

Price Action Analysis Toolkit Development (Part 26): Pin Bar, Engulfing Patterns and RSI Divergence (Multi-Pattern) Tool

Aligned with our goal of developing practical price-action tools, this article explores the creation of an EA that detects pin bar and engulfing patterns, using RSI divergence as a confirmation trigger before generating any trading signals.
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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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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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The Kalman Filter for Forex Mean-Reversion Strategies

The Kalman Filter for Forex Mean-Reversion Strategies

The Kalman filter is a recursive algorithm used in algorithmic trading to estimate the true state of a financial time series by filtering out noise from price movements. It dynamically updates predictions based on new market data, making it valuable for adaptive strategies like mean reversion. This article first introduces the Kalman filter, covering its calculation and implementation. Next, we apply the filter to a classic mean-reversion forex strategy as an example. Finally, we conduct various statistical analyses by comparing the filter with a moving average across different forex pairs.
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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.
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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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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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.
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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.
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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.
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.
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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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.
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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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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.
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.
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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.
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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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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.