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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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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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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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.
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 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.
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Developing a Replay System — Market simulation (Part 14): Birth of the SIMULATOR (IV)

Developing a Replay System — Market simulation (Part 14): Birth of the SIMULATOR (IV)

In this article we will continue the simulator development stage. this time we will see how to effectively create a RANDOM WALK type movement. This type of movement is very intriguing because it forms the basis of everything that happens in the capital market. In addition, we will begin to understand some concepts that are fundamental to those conducting market analysis.
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Creating Custom Indicators in MQL5 (Part 5): WaveTrend Crossover Evolution Using Canvas for Fog Gradients, Signal Bubbles, and Risk Management

Creating Custom Indicators in MQL5 (Part 5): WaveTrend Crossover Evolution Using Canvas for Fog Gradients, Signal Bubbles, and Risk Management

In this article, we enhance the Smart WaveTrend Crossover indicator in MQL5 by integrating canvas-based drawing for fog gradient overlays, signal boxes that detect breakouts, and customizable buy/sell bubbles or triangles for visual alerts. We incorporate risk management features with dynamic take-profit and stop-loss levels calculated via candle multipliers or percentages, displayed through lines and a table, alongside options for trend filtering and box extensions.
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From Novice to Expert: Animated News Headline Using MQL5 (I)

From Novice to Expert: Animated News Headline Using MQL5 (I)

News accessibility is a critical factor when trading on the MetaTrader 5 terminal. While numerous news APIs are available, many traders face challenges in accessing and integrating them effectively into their trading environment. In this discussion, we aim to develop a streamlined solution that brings news directly onto the chart—where it’s most needed. We'll accomplish this by building a News Headline Expert Advisor that monitors and displays real-time news updates from API sources.
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Exploring Conformal Forecasting of Financial Time Series

Exploring Conformal Forecasting of Financial Time Series

In this article, we will consider conformal predictions and the MAPIE library that implements them. This approach is one of the most modern ones in machine learning and allows us to focus on risk management for existing diverse machine learning models. Conformal predictions, by themselves, are not a way to find patterns in data. They only determine the degree of confidence of existing models in predicting specific examples and allow filtering for reliable predictions.
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Python-MetaTrader 5 Strategy Tester (Part 02): Dealing with Bars, Ticks, and Overloading Built-in Functions in a Simulator

Python-MetaTrader 5 Strategy Tester (Part 02): Dealing with Bars, Ticks, and Overloading Built-in Functions in a Simulator

In this article, we introduce functions similar to those provided by the Python-MetaTrader 5 module, providing a simulator with a familiar interface and a custom way of handling bars and ticks internally.
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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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Developing A Swing Entries Monitoring (EA)

Developing A Swing Entries Monitoring (EA)

As the year approaches its end, long-term traders often reflect on market history to analyze its behavior and trends, aiming to project potential future movements. In this article, we will explore the development of a long-term entry monitoring Expert Advisor (EA) using MQL5. The objective is to address the challenge of missed long-term trading opportunities caused by manual trading and the absence of automated monitoring systems. We'll use one of the most prominently traded pairs as an example to strategize and develop our solution effectively.
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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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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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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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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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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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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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Price Action Analysis Toolkit Development (Part 45): Creating a Dynamic Level-Analysis Panel in MQL5

Price Action Analysis Toolkit Development (Part 45): Creating a Dynamic Level-Analysis Panel in MQL5

In this article, we explore a powerful MQL5 tool that let's you test any price level you desire with just one click. Simply enter your chosen level and press analyze, the EA instantly scans historical data, highlights every touch and breakout on the chart, and displays statistics in a clean, organized dashboard. You'll see exactly how often price respected or broke through your level, and whether it behaved more like support or resistance. Continue reading to explore the detailed procedure.
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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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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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Quantitative Analysis of Trends: Collecting Statistics in Python

Quantitative Analysis of Trends: Collecting Statistics in Python

What is quantitative trend analysis in the Forex market? We collect statistics on trends, their magnitude and distribution across the EURUSD currency pair. How quantitative trend analysis can help you create a profitable trading expert advisor.
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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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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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Implementing Practical Modules from Other Languages in MQL5 (Part 03): Schedule Module from Python, the OnTimer Event on Steroids

Implementing Practical Modules from Other Languages in MQL5 (Part 03): Schedule Module from Python, the OnTimer Event on Steroids

The schedule module in Python offers a simple way to schedule repeated tasks. While MQL5 lacks a built-in equivalent, in this article we’ll implement a similar library to make it easier to set up timed events in MetaTrader 5.
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Statistical Arbitrage Through Cointegrated Stocks (Part 4): Real-time Model Updating

Statistical Arbitrage Through Cointegrated Stocks (Part 4): Real-time Model Updating

This article describes a simple but comprehensive statistical arbitrage pipeline for trading a basket of cointegrated stocks. It includes a fully functional Python script for data download and storage; correlation, cointegration, and stationarity tests, along with a sample Metatrader 5 Service implementation for database updating, and the respective Expert Advisor. Some design choices are documented here for reference and for helping in the experiment replication.
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Developing a quality factor for Expert Advisors

Developing a quality factor for Expert Advisors

In this article, we will see how to develop a quality score that your Expert Advisor can display in the strategy tester. We will look at two well-known calculation methods – Van Tharp and Sunny Harris.
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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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Hidden Markov Models in Machine Learning-Based Trading Systems

Hidden Markov Models in Machine Learning-Based Trading Systems

Hidden Markov Models (HMMs) are a powerful class of probabilistic models designed to analyze sequential data, where observed events depend on some sequence of unobserved (hidden) states that form a Markov process. The main assumptions of HMM include the Markov property for hidden states, meaning that the probability of transition to the next state depends only on the current state, and the independence of observations given knowledge of the current hidden state.
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Overcoming The Limitation of Machine Learning (Part 6): Effective Memory Cross Validation

Overcoming The Limitation of Machine Learning (Part 6): Effective Memory Cross Validation

In this discussion, we contrast the classical approach to time series cross-validation with modern alternatives that challenge its core assumptions. We expose key blind spots in the traditional method—especially its failure to account for evolving market conditions. To address these gaps, we introduce Effective Memory Cross-Validation (EMCV), a domain-aware approach that questions the long-held belief that more historical data always improves performance.
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Analyzing Overbought and Oversold Trends Via Chaos Theory Approaches

Analyzing Overbought and Oversold Trends Via Chaos Theory Approaches

We determine the overbought and oversold condition of the market according to chaos theory: integrating the principles of chaos theory, fractal geometry and neural networks to forecast financial markets. The study demonstrates the use of the Lyapunov exponent as a measure of market randomness and the dynamic adaptation of trading signals. The methodology includes an algorithm for generating fractal noise, hyperbolic tangent activation, and moment optimization.
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Low-Frequency Quantitative Strategies in Metatrader 5: (Part 2) Backtesting a Lead/Lag Analysis in SQL and in Metatrader 5

Low-Frequency Quantitative Strategies in Metatrader 5: (Part 2) Backtesting a Lead/Lag Analysis in SQL and in Metatrader 5

The article describes a complete pipeline that uses data analysis for finding low-frequency lead/lag trading opportunities. It goes into building a cross-correlation-based Lead/Lag analyser step-by-step, with special attention to the most common errors beginners may commit while developing cross-asset diffusion queries. After screening dozens of cointegrated and correlated pairs, a trading candidate pair is chosen, and its tradeability is evaluated in a pure SQL backtest. Once it is qualified, the strategy is backtested on the MetaTester for parameter optimization. The Expert Advisor with respective backtest settings and optimization inputs is provided, along with Python and SQL scripts.
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MQL5 Wizard Techniques you should know (Part 51): Reinforcement Learning with SAC

MQL5 Wizard Techniques you should know (Part 51): Reinforcement Learning with SAC

Soft Actor Critic is a Reinforcement Learning algorithm that utilizes 3 neural networks. An actor network and 2 critic networks. These machine learning models are paired in a master slave partnership where the critics are modelled to improve the forecast accuracy of the actor network. While also introducing ONNX in these series, we explore how these ideas could be put to test as a custom signal of a wizard assembled Expert Advisor.
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From Novice to Expert: Animated News Headline Using MQL5 (IV) — Locally hosted AI model market insights

From Novice to Expert: Animated News Headline Using MQL5 (IV) — Locally hosted AI model market insights

In today's discussion, we explore how to self-host open-source AI models and use them to generate market insights. This forms part of our ongoing effort to expand the News Headline EA, introducing an AI Insights Lane that transforms it into a multi-integration assistive tool. The upgraded EA aims to keep traders informed through calendar events, financial breaking news, technical indicators, and now AI-generated market perspectives—offering timely, diverse, and intelligent support to trading decisions. Join the conversation as we explore practical integration strategies and how MQL5 can collaborate with external resources to build a powerful and intelligent trading work terminal.
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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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CFTC Data Mining in Python and Building an AI Model

CFTC Data Mining in Python and Building an AI Model

Let's try mining CFTC data, downloading COT and TFF reports via Python, connecting all this with MetaTrader 5 quotes and an AI model, and get forecasts. What are COT reports in the Forex market? How to use COT and TFF reports for forecasting?
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MetaTrader 5 Machine Learning Blueprint (Part 13):  Implementing Bet Sizing in MQL5

MetaTrader 5 Machine Learning Blueprint (Part 13): Implementing Bet Sizing in MQL5

We build a production MQL5 bet‑sizing toolkit: utilities, snippets, and user‑level functions that mirror the Python originals. The methods cover probability‑to‑size mapping with overlap correction, dynamic forecast‑price sizing (calibrated sigmoid/power with limit price), occupancy‑based budgeting, and mixture‑model reserve sizing (EF3M). The result is a signed [−1, ..., 1] position plus diagnostics you can plug directly into order logic.
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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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Creating Custom Indicators in MQL5 (Part 10): Enhancing the Footprint Chart with Per-Bar Volume Sentiment Information Box

Creating Custom Indicators in MQL5 (Part 10): Enhancing the Footprint Chart with Per-Bar Volume Sentiment Information Box

The article enhances an MQL5 footprint indicator with a compact box above each candle that summarizes net delta, total volume, and buy/sell percentages. We implement supersampled anti‑aliased rendering, rounded corners via arc and quadrilateral rasterization, and per‑pixel alpha compositing. Supporting utilities include ARGB conversion, scanline fills, and box‑filter downsampling. The box delivers fast sentiment reads that stay legible across zoom levels.
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Swap Arbitrage in Forex: Building a Synthetic Portfolio and Generating a Consistent Swap Flow

Swap Arbitrage in Forex: Building a Synthetic Portfolio and Generating a Consistent Swap Flow

Do you want to know how to benefit from the difference in interest rates? This article considers how to use swap arbitrage in Forex to earn stable profit every night, creating a portfolio that is resistant to market fluctuations.