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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Integrating Computer Vision into Trading in MQL5 (Part 1): Creating Basic Functions

Integrating Computer Vision into Trading in MQL5 (Part 1): Creating Basic Functions

The EURUSD forecasting system with the use of computer vision and deep learning. Learn how convolutional neural networks can recognize complex price patterns in the foreign exchange market and predict exchange rate movements with up to 54% accuracy. The article shares the methodology for creating an algorithm that uses artificial intelligence technologies for visual analysis of charts instead of traditional technical indicators. The author demonstrates the process of transforming price data into "images", their processing by a neural network, and a unique opportunity to peer into the "consciousness" of AI through activation maps and attention heatmaps. Practical Python code using the MetaTrader 5 library allows readers to reproduce the system and apply it in their own trading.
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Statistical Arbitrage Through Cointegrated Stocks (Part 2): Expert Advisor, Backtests, and Optimization

Statistical Arbitrage Through Cointegrated Stocks (Part 2): Expert Advisor, Backtests, and Optimization

This article presents a sample Expert Advisor implementation for trading a basket of four Nasdaq stocks. The stocks were initially filtered based on Pearson correlation tests. The filtered group was then tested for cointegration with Johansen tests. Finally, the cointegrated spread was tested for stationarity with the ADF and KPSS tests. Here we will see some notes about this process and the results of the backtests after a small optimization.
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Developing a Replay System — Market simulation (Part 09): Custom events

Developing a Replay System — Market simulation (Part 09): Custom events

Here we'll see how custom events are triggered and how the indicator reports the state of the replay/simulation service.
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Exploring Machine Learning in Unidirectional Trend Trading Using Gold as a Case Study

Exploring Machine Learning in Unidirectional Trend Trading Using Gold as a Case Study

This article discusses an approach to trading only in the chosen direction (buy or sell). For this purpose, the technique of causal inference and machine learning are used.
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Data Science and ML (Part 46): Stock Markets Forecasting Using N-BEATS in Python

Data Science and ML (Part 46): Stock Markets Forecasting Using N-BEATS in Python

N-BEATS is a revolutionary deep learning model designed for time series forecasting. It was released to surpass classical models for time series forecasting such as ARIMA, PROPHET, VAR, etc. In this article, we are going to discuss this model and use it in predicting the stock market.
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Algorithmic Trading Strategies: AI and Its Road to Golden Pinnacles

Algorithmic Trading Strategies: AI and Its Road to Golden Pinnacles

This article demonstrates an approach to creating trading strategies for gold using machine learning. Considering the proposed approach to the analysis and forecasting of time series from different angles, it is possible to determine its advantages and disadvantages in comparison with other ways of creating trading systems which are based solely on the analysis and forecasting of financial time series.
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Population ADAM (Adaptive Moment Estimation)

Population ADAM (Adaptive Moment Estimation)

The article presents the transformation of the well-known and popular ADAM gradient optimization method into a population algorithm and its modification with the introduction of hybrid individuals. The new approach allows creating agents that combine elements of successful decisions using probability distribution. The key innovation is the formation of hybrid population individuals that adaptively accumulate information from the most promising solutions, increasing the efficiency of search in complex multidimensional spaces.
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Developing a multi-currency Expert Advisor (Part 8): Load testing and handling a new bar

Developing a multi-currency Expert Advisor (Part 8): Load testing and handling a new bar

As we progressed, we used more and more simultaneously running instances of trading strategies in one EA. Let's try to figure out how many instances we can get to before we hit resource limitations.
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Price Action Analysis Toolkit Development (Part 37): Sentiment Tilt Meter

Price Action Analysis Toolkit Development (Part 37): Sentiment Tilt Meter

Market sentiment is one of the most overlooked yet powerful forces influencing price movement. While most traders rely on lagging indicators or guesswork, the Sentiment Tilt Meter (STM) EA transforms raw market data into clear, visual guidance, showing whether the market is leaning bullish, bearish, or staying neutral in real-time. This makes it easier to confirm trades, avoid false entries, and time market participation more effectively.
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Elements of correlation analysis in MQL5: Pearson chi-square test of independence and correlation ratio

Elements of correlation analysis in MQL5: Pearson chi-square test of independence and correlation ratio

The article observes classical tools of correlation analysis. An emphasis is made on brief theoretical background, as well as on the practical implementation of the Pearson chi-square test of independence and the correlation ratio.
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From Novice to Expert: Animated News Headline Using MQL5 (III) — Indicator Insights

From Novice to Expert: Animated News Headline Using MQL5 (III) — Indicator Insights

In this article, we’ll advance the News Headline EA by introducing a dedicated indicator insights lane—a compact, on-chart display of key technical signals generated from popular indicators such as RSI, MACD, Stochastic, and CCI. This approach eliminates the need for multiple indicator subwindows on the MetaTrader 5 terminal, keeping your workspace clean and efficient. By leveraging the MQL5 API to access indicator data in the background, we can process and visualize market insights in real-time using custom logic. Join us as we explore how to manipulate indicator data in MQL5 to create an intelligent and space-saving scrolling insights system, all within a single horizontal lane on your trading chart.
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Atomic Orbital Search (AOS) algorithm

Atomic Orbital Search (AOS) algorithm

The article considers the Atomic Orbital Search (AOS) algorithm, which uses the concepts of the atomic orbital model to simulate the search for solutions. The algorithm is based on probability distributions and the dynamics of interactions in the atom. The article discusses in detail the mathematical aspects of AOS, including updating the positions of candidate solutions and the mechanisms of energy absorption and release. AOS opens new horizons for applying quantum principles to computing problems by offering an innovative approach to optimization.
Developing a Replay System — Market simulation (Part 10): Using only real data for Replay
Developing a Replay System — Market simulation (Part 10): Using only real data for Replay

Developing a Replay System — Market simulation (Part 10): Using only real data for Replay

Here we will look at how we can use more reliable data (traded ticks) in the replay system without worrying about whether it is adjusted or not.
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MQL5 Trading Tools (Part 5): Creating a Rolling Ticker Tape for Real-Time Symbol Monitoring

MQL5 Trading Tools (Part 5): Creating a Rolling Ticker Tape for Real-Time Symbol Monitoring

In this article, we develop a rolling ticker tape in MQL5 for real-time monitoring of multiple symbols, displaying bid prices, spreads, and daily percentage changes with scrolling effects. We implement customizable fonts, colors, and scroll speeds to highlight price movements and trends effectively.
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Python-MetaTrader 5 Strategy Tester (Part 04): Tester 101

Python-MetaTrader 5 Strategy Tester (Part 04): Tester 101

In this fascinating article, we build our very first trading robot in the simulator and run a strategy testing action that resembles how the MetaTrader 5 strategy tester works, then compare the outcome produced in a custom simulation against our favorite terminal.
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Developing a Replay System (Part 76): New Chart Trade (III)

Developing a Replay System (Part 76): New Chart Trade (III)

In this article, we'll look at how the code of DispatchMessage, missing from the previous article, works. We will laso introduce the topic of the next article. For this reason, it is important to understand how this code works before moving on to the next topic. The content presented here is intended solely for educational purposes. Under no circumstances should the application be viewed for any purpose other than to learn and master the concepts presented.
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Build Self Optimizing Expert Advisors in MQL5 (Part 7): Trading With Multiple Periods At Once

Build Self Optimizing Expert Advisors in MQL5 (Part 7): Trading With Multiple Periods At Once

In this series of articles, we have considered multiple different ways of identifying the best period to use our technical indicators with. Today, we shall demonstrate to the reader how they can instead perform the opposite logic, that is to say, instead of picking the single best period to use, we will demonstrate to the reader how to employ all available periods effectively. This approach reduces the amount of data discarded, and offers alternative use cases for machine learning algorithms beyond ordinary price prediction.
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Matrix Factorization: A more practical modeling

Matrix Factorization: A more practical modeling

You might not have noticed that the matrix modeling was a little strange, since only columns were specified, not rows and columns. This looks very strange when reading the code that performs matrix factorizations. If you were expecting to see the rows and columns listed, you might get confused when trying to factorize. Moreover, this matrix modeling method is not the best. This is because when we model matrices in this way, we encounter some limitations that force us to use other methods or functions that would not be necessary if the modeling were done in a more appropriate way.
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MetaTrader tick info access from MQL5 services to Python application using sockets

MetaTrader tick info access from MQL5 services to Python application using sockets

Sometimes everything is not programmable in the MQL5 language. And even if it is possible to convert existing advanced libraries in MQL5, it would be time-consuming. This article tries to show that we can bypass Windows OS dependency by transporting tick information such as bid, ask and time with MetaTrader services to a Python application using sockets.
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Developing a Replay System — Market simulation (Part 08): Locking the indicator

Developing a Replay System — Market simulation (Part 08): Locking the indicator

In this article, we will look at how to lock the indicator while simply using the MQL5 language, and we will do it in a very interesting and amazing way.
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Cross-validation and basics of causal inference in CatBoost models, export to ONNX format

Cross-validation and basics of causal inference in CatBoost models, export to ONNX format

The article proposes the method of creating bots using machine learning.
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Data Science and Machine Learning (Part 16): A Refreshing Look at Decision Trees

Data Science and Machine Learning (Part 16): A Refreshing Look at Decision Trees

Dive into the intricate world of decision trees in the latest installment of our Data Science and Machine Learning series. Tailored for traders seeking strategic insights, this article serves as a comprehensive recap, shedding light on the powerful role decision trees play in the analysis of market trends. Explore the roots and branches of these algorithmic trees, unlocking their potential to enhance your trading decisions. Join us for a refreshing perspective on decision trees and discover how they can be your allies in navigating the complexities of financial markets.
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Time Evolution Travel Algorithm (TETA)

Time Evolution Travel Algorithm (TETA)

This is my own algorithm. The article presents the Time Evolution Travel Algorithm (TETA) inspired by the concept of parallel universes and time streams. The basic idea of the algorithm is that, although time travel in the conventional sense is impossible, we can choose a sequence of events that lead to different realities.
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MQL5 Wizard Techniques you should know (Part 24): Moving Averages

MQL5 Wizard Techniques you should know (Part 24): Moving Averages

Moving Averages are a very common indicator that are used and understood by most Traders. We explore possible use cases that may not be so common within MQL5 Wizard assembled Expert Advisors.
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Evolutionary trading algorithm with reinforcement learning and extinction of feeble individuals (ETARE)

Evolutionary trading algorithm with reinforcement learning and extinction of feeble individuals (ETARE)

In this article, I introduce an innovative trading algorithm that combines evolutionary algorithms with deep reinforcement learning for Forex trading. The algorithm uses the mechanism of extinction of inefficient individuals to optimize the trading strategy.
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Quantitative approach to risk management: Applying VaR model to optimize multi-currency portfolio using Python and MetaTrader 5

Quantitative approach to risk management: Applying VaR model to optimize multi-currency portfolio using Python and MetaTrader 5

This article explores the potential of the Value at Risk (VaR) model for multi-currency portfolio optimization. Using the power of Python and the functionality of MetaTrader 5, we demonstrate how to implement VaR analysis for efficient capital allocation and position management. From theoretical foundations to practical implementation, the article covers all aspects of applying one of the most robust risk calculation systems – VaR – in algorithmic trading.
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MQL5 Wizard Techniques you should know (Part 26): Moving Averages and the Hurst Exponent

MQL5 Wizard Techniques you should know (Part 26): Moving Averages and the Hurst Exponent

The Hurst Exponent is a measure of how much a time series auto-correlates over the long term. It is understood to be capturing the long-term properties of a time series and therefore carries some weight in time series analysis even outside of economic/ financial time series. We however, focus on its potential benefit to traders by examining how this metric could be paired with moving averages to build a potentially robust signal.
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Alternative risk return metrics in MQL5

Alternative risk return metrics in MQL5

In this article we present the implementation of several risk return metrics billed as alternatives to the Sharpe ratio and examine hypothetical equity curves to analyze their characteristics.
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Fractal-Based Algorithm (FBA)

Fractal-Based Algorithm (FBA)

The article presents a new metaheuristic method based on a fractal approach to partitioning the search space for solving optimization problems. The algorithm sequentially identifies and separates promising areas, creating a self-similar fractal structure that concentrates computing resources on the most promising areas. A unique mutation mechanism aimed at better solutions ensures an optimal balance between exploration and exploitation of the search space, significantly increasing the efficiency of the algorithm.
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Developing a Replay System (Part 42): Chart Trade Project (I)

Developing a Replay System (Part 42): Chart Trade Project (I)

Let's create something more interesting. I don't want to spoil the surprise, so follow the article for a better understanding. From the very beginning of this series on developing the replay/simulator system, I was saying that the idea is to use the MetaTrader 5 platform in the same way both in the system we are developing and in the real market. It is important that this is done properly. No one wants to train and learn to fight using one tool while having to use another one during the fight.
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Population optimization algorithms: Differential Evolution (DE)

Population optimization algorithms: Differential Evolution (DE)

In this article, we will consider the algorithm that demonstrates the most controversial results of all those discussed previously - the differential evolution (DE) algorithm.
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Developing a Replay System — Market simulation (Part 13): Birth of the SIMULATOR (III)

Developing a Replay System — Market simulation (Part 13): Birth of the SIMULATOR (III)

Here we will simplify a few elements related to the work in the next article. I'll also explain how you can visualize what the simulator generates in terms of randomness.
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Forex Arbitrage Trading: A Matrix Trading System for Return to Fair Value with Risk Control

Forex Arbitrage Trading: A Matrix Trading System for Return to Fair Value with Risk Control

The article contains a detailed description of the cross-rate calculation algorithm, a visualization of the imbalance matrix, and recommendations for optimally setting the MinDiscrepancy and MaxRisk parameters for efficient trading. The system automatically calculates the "fair value" of each currency pair using cross rates, generating buy signals in case of negative deviations and sell signals in case of positive ones.
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Developing a Replay System — Market simulation (Part 24): FOREX (V)

Developing a Replay System — Market simulation (Part 24): FOREX (V)

Today we will remove a limitation that has been preventing simulations based on the Last price and will introduce a new entry point specifically for this type of simulation. The entire operating mechanism will be based on the principles of the forex market. The main difference in this procedure is the separation of Bid and Last simulations. However, it is important to note that the methodology used to randomize the time and adjust it to be compatible with the C_Replay class remains identical in both simulations. This is good because changes in one mode lead to automatic improvements in the other, especially when it comes to handling time between ticks.
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Example of Stochastic Optimization and Optimal Control

Example of Stochastic Optimization and Optimal Control

This Expert Advisor, named SMOC (likely standing for Stochastic Model Optimal Control), is a simple example of an advanced algorithmic trading system for MetaTrader 5. It uses a combination of technical indicators, model predictive control, and dynamic risk management to make trading decisions. The EA incorporates adaptive parameters, volatility-based position sizing, and trend analysis to optimize its performance across varying market conditions.
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Data Science and ML (Part 43): Hidden Patterns Detection in Indicators Data Using Latent Gaussian Mixture Models (LGMM)

Data Science and ML (Part 43): Hidden Patterns Detection in Indicators Data Using Latent Gaussian Mixture Models (LGMM)

Have you ever looked at the chart and felt that strange sensation… that there’s a pattern hidden just beneath the surface? A secret code that might reveal where prices are headed if only you could crack it? Meet LGMM, the Market’s Hidden Pattern Detector. A machine learning model that helps identify those hidden patterns in the market.
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Market Simulation (Part 20): First steps with SQL (III)

Market Simulation (Part 20): First steps with SQL (III)

Although we can perform operations on a database containing about 10 records, the material is absorbed much better when we work with a file that contains more than 15 thousand records. That is, if we tried to create such a database manually, this task would be enormous. However, it is difficult to find such a database, even for educational purposes, that is available for download. But in reality, we don’t need to resort to that — we can use MetaTrader 5 to create a database for ourselves. In today's article, we will look at how to do this.
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Developing a Replay System (Part 73): An Unusual Communication (II)

Developing a Replay System (Part 73): An Unusual Communication (II)

In this article, we will look at how to transmit information in real time between the indicator and the service, and also understand why problems may arise when changing the timeframe and how to solve them. As a bonus, you will get access to the latest version of the replay /simulation app.
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MQL5 Wizard Techniques you should know (Part 43): Reinforcement Learning with SARSA

MQL5 Wizard Techniques you should know (Part 43): Reinforcement Learning with SARSA

SARSA, which is an abbreviation for State-Action-Reward-State-Action is another algorithm that can be used when implementing reinforcement learning. So, as we saw with Q-Learning and DQN, we look into how this could be explored and implemented as an independent model rather than just a training mechanism, in wizard assembled Expert Advisors.
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MQL5 Wizard Techniques you should know (Part 49): Reinforcement Learning with Proximal Policy Optimization

MQL5 Wizard Techniques you should know (Part 49): Reinforcement Learning with Proximal Policy Optimization

Proximal Policy Optimization is another algorithm in reinforcement learning that updates the policy, often in network form, in very small incremental steps to ensure the model stability. We examine how this could be of use, as we have with previous articles, in a wizard assembled Expert Advisor.