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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The case for using Hospital-Performance Data with Perceptrons, this Q4, in weighing SPDR XLV's next Performance

The case for using Hospital-Performance Data with Perceptrons, this Q4, in weighing SPDR XLV's next Performance

XLV is SPDR healthcare ETF and in an age where it is common to be bombarded by a wide array of traditional news items plus social media feeds, it can be pressing to select a data set for use with a model. We try to tackle this problem for this ETF by sizing up some of its critical data sets in MQL5.
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MQL5 Wizard Techniques you should know (Part 90): Fenwick Tree Money Management with 1D CNN in MQL5

MQL5 Wizard Techniques you should know (Part 90): Fenwick Tree Money Management with 1D CNN in MQL5

This article implements a Fenwick Tree (Binary Indexed Tree) for volume-aware money management inside an MQL5 Wizard Expert Advisor. We structure cumulative volume in O(log n) and apply four scaling modes—linear, conservative, aggressive, and mean-reversion—optionally gated by a lightweight 1D CNN. Practical tests compare the algorithm alone versus the CNN‑filtered approach to illustrate adaptive lot sizing and risk control under varying volume topologies.
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Market Simulation (Part 22): Getting Started with SQL (V)

Market Simulation (Part 22): Getting Started with SQL (V)

Before you give up and decide to abandon learning SQL, allow me to remind you, dear readers, that here we are still using only the most basic elements. We have not yet looked at some of SQL's capabilities. Once you understand them, you will see that SQL is far more practical than it seems. Although, most likely, we will eventually change the direction of what we are building, because the creation process is dynamic. We will show a little more about creating different things in SQL, because this is truly important and useful for you. Simply thinking that you are more capable than an entire community of programmers and developers will only lead to wasted time and opportunities. Do not worry, because what comes next will be even more interesting.
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MQL5 Trading Tools (Part 39): Adding a Pinned-Tools Ribbon for Quick Access to Favorite Tools

MQL5 Trading Tools (Part 39): Adding a Pinned-Tools Ribbon for Quick Access to Favorite Tools

We add a pinned-tools ribbon: a floating bar that exposes frequently used tools for one-click access without reopening the sidebar. The article implements the ordered pin set and its API, an anti-aliased pushpin control in the flyout, and the ribbon with offscreen clipping, user-resizable width, and horizontal scrolling. The result is faster activation of favorite tools from a draggable, resizable ribbon on the chart.
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Building an Object-Oriented Z-Score Statistical Arbitrage Engine in MQL5

Building an Object-Oriented Z-Score Statistical Arbitrage Engine in MQL5

This article shows how to implement a production Z-Score engine in MQL5 using an object-oriented include file, the library computes a rolling mean and population standard deviation, exposes a shift parameter for historical queries, and avoids redundant tick work by running on bar close. An Expert Advisor executes rule-based entries at positive/negative sigma thresholds and closes on mean reversion; a custom indicator provides visual verification.
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Developing a Replay System (Part 39): Paving the Path (III)

Developing a Replay System (Part 39): Paving the Path (III)

Before we proceed to the second stage of development, we need to revise some ideas. Do you know how to make MQL5 do what you need? Have you ever tried to go beyond what is contained in the documentation? If not, then get ready. Because we will be doing something that most people don't normally do.
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Market Simulation (Part 24): Position View (II)

Market Simulation (Part 24): Position View (II)

In this article, I will show how to use an indicator to track open positions on the trading server in the simplest and most practical way possible. I am doing this step by step to show that you do not necessarily have to move all of this into an Expert Advisor. Many of you have probably become used to doing that for one reason or another. In fact, that is not really justified, because as this implementation evolves, it will become clear that you can create or implement different types of indicators for this purpose.
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Building a JSON Trade Report Exporter in Pure MQL5

Building a JSON Trade Report Exporter in Pure MQL5

A refined MQL5 script exports trade history to a well‑formed JSON file in MQL5/Files/, reconstructing trades from deals by position ID and recovering stop loss and take profit via a two‑pass lookup that falls back closed to the originating order. It includes a dedicated JSON serializer and computes R‑multiple, pip profit, and duration. The result loads cleanly in Python, R, or Excel without custom parsing.
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Market Simulation (Part 24): Getting Started with SQL (VII)

Market Simulation (Part 24): Getting Started with SQL (VII)

In the previous article, we completed the necessary introduction to SQL. And, in my opinion, we properly clarified what we wanted to show and explain about SQL. This was done so that anyone who comes to look at the market replay/simulation system being built can at least get an idea of what may be happening there. The point is that there is no sense in programming things that SQL handles perfectly.
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Exchange Market Algorithm (EMA)

Exchange Market Algorithm (EMA)

The article presents a detailed analysis of the Exchange Market Algorithm (EMA) inspired by the behavior of stock market traders. The algorithm simulates stock trading, where market participants with varying levels of success employ different strategies to maximize profits.
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Bison Algorithm (BIA)

Bison Algorithm (BIA)

A new optimization method, the Bison Algorithm (BIA), uses two strategies, inspired by the behavior of bison, for solving continuous problems with a single objective function. The key features of BIA are two fundamental principles borrowed from the behavior of bison: the ability to move dynamically and a defensive strategy.
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MQL5 Trading Toolkit (Part 7): Expanding the History Management EX5 Library with the Last Canceled Pending Order Functions

MQL5 Trading Toolkit (Part 7): Expanding the History Management EX5 Library with the Last Canceled Pending Order Functions

Learn how to complete the creation of the final module in the History Manager EX5 library, focusing on the functions responsible for handling the most recently canceled pending order. This will provide you with the tools to efficiently retrieve and store key details related to canceled pending orders with MQL5.
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Defining your Edge (Part 2): Using Divergence Mapping and a Temporal Fusion Transformer in a Trading Robot

Defining your Edge (Part 2): Using Divergence Mapping and a Temporal Fusion Transformer in a Trading Robot

In this article we make the case for merging Divergence Mapping with a Temporal Fusion Proxy in a Trading Robot. Rather than depending on lagging price confirmations, the Divergence Mapping's thesis is that acting like a structural sensor can help identify hidden momentum shifts from price action and indicator anomalies. To establish how these anomalies are interpreted over time we use a Temporal Fusion Transformer proxy. This network incorporates historical context to weigh developing trends such that merging it with Divergence Mapping should set us up to spot shifts in accumulation and distribution before price breakouts.
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Duelist Algorithm

Duelist Algorithm

What if your trading strategies could learn from each other, like real fighters? Duelist Algorithm is a new optimization method where trading system parameters literally duel for the right to be called the best.
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MQL5 Trading Tools (Part 29): Step-by-Step Butterfly Animation on Canvas

MQL5 Trading Tools (Part 29): Step-by-Step Butterfly Animation on Canvas

In this article, we expand our butterfly animation program with a four-stage animation pipeline: sequential curve drawing, smooth wing fill fading, detailed body rendering, and continuous flight. We implement a timer-driven state machine, four oscillators for wing flapping, vertical bobbing, horizontal sway, and tilt, as well as a neon glow around the wing outlines and a cyclical color change based on hue. You will learn how to structure these effects on the MetaTrader 5 canvas for clean and controlled playback.
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Elite Crystal Evolution Algorithm (CEO-inspired): Theory

Elite Crystal Evolution Algorithm (CEO-inspired): Theory

A new original population-based algorithm, ECEA, is presented. Inspired by the process of water freezing, it adapts ideas from the Crystal Energy Optimizer (CEO) algorithm, which uses graph-based search, for general optimization problems. The algorithm uses a dynamic elite group, three search strategies, and a periodic diversification mechanism.
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Introduction to MQL5 (Part 40): Beginner Guide to File Handling in MQL5 (II)

Introduction to MQL5 (Part 40): Beginner Guide to File Handling in MQL5 (II)

Create a CSV trading journal in MQL5 by reading account history over a defined period and writing structured records to file. The article explains deal counting, ticket retrieval, symbol and order type decoding, and capturing entry (lot, time, price, SL/TP) and exit (time, price, profit, result) data with dynamic arrays. The result is an organized, persistent log suitable for analysis and reporting.
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Nonlinear OHLC Features Derived from Elliptic Curves

Nonlinear OHLC Features Derived from Elliptic Curves

The article discusses the projection of EURUSD daily candlesticks onto the secp256k1 elliptic curve and the extraction of 96 features (EC+TA) to predict the direction of the next candlestick in CatBoost. The price mapping to the curve and the training pipeline on 2,000 D1 bars are shown; the full model achieves a test AUC of 0.6508, with EC features contributing 60.6%. The materials are suitable for reproduction in Python/MetaTrader 5.
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Population optimization algorithms: Resistance to getting stuck in local extrema (Part I)

Population optimization algorithms: Resistance to getting stuck in local extrema (Part I)

This article presents a unique experiment that aims to examine the behavior of population optimization algorithms in the context of their ability to efficiently escape local minima when population diversity is low and reach global maxima. Working in this direction will provide further insight into which specific algorithms can successfully continue their search using coordinates set by the user as a starting point, and what factors influence their success.
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Implementation of a table model in MQL5: Applying the MVC concept

Implementation of a table model in MQL5: Applying the MVC concept

In this article, we look at the process of developing a table model in MQL5 using the MVC (Model-View-Controller) architectural pattern to separate data logic, presentation, and control, enabling structured, flexible, and scalable code. We consider implementation of classes for building a table model, including the use of linked lists for storing data.
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MQL5 Trading Tools (Part 40): Adding SQLite Persistence and Per-Timeframe Visibility to the Canvas Drawing Layer

MQL5 Trading Tools (Part 40): Adding SQLite Persistence and Per-Timeframe Visibility to the Canvas Drawing Layer

We add SQLite persistence to the canvas tools, saving every drawing and the entire UI session per symbol, then restoring them on startup so the workspace resumes exactly where you left it. The article builds versioned object serialization, a load/save lifecycle with dirty writes, and a timeframe-visibility editor that drives render-time filtering. The toolkit also runs as an indicator, so it can sit alongside other indicators or an Expert Advisor.
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Developing a Replay System (Part 34): Order System (III)

Developing a Replay System (Part 34): Order System (III)

In this article, we will complete the first phase of construction. Although this part is fairly quick to complete, I will cover details that were not discussed previously. I will explain some points that many do not understand. Do you know why you have to press the Shift or Ctrl key?
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Building a Broker-Agnostic Symbol Resolution Layer in MQL5

Building a Broker-Agnostic Symbol Resolution Layer in MQL5

We implement a symbol resolution framework that abstracts broker naming differences in MetaTrader 5. Using a persistent mapping store, layered resolution with validation, a hash-indexed registry, and a cache, it returns selectable symbols with live market data and logs unresolved cases. Practically, you can deploy the same EA across brokers and keep symbol access consistent at low runtime cost.
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Developing a Replay System (Part 41): Starting the second phase (II)

Developing a Replay System (Part 41): Starting the second phase (II)

If everything seemed right to you up to this point, it means you're not really thinking about the long term, when you start developing applications. Over time you will no longer need to program new applications, you will just have to make them work together. So let's see how to finish assembling the mouse indicator.
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Overcoming Accessibility Problems in MQL5 Trading Tools (Part I): How to Add Contextual Voice Alerts in MQL5 Indicators

Overcoming Accessibility Problems in MQL5 Trading Tools (Part I): How to Add Contextual Voice Alerts in MQL5 Indicators

This article explores an accessibility-focused enhancement that goes beyond default terminal alerts by leveraging MQL5 resource management to deliver contextual voice feedback. Instead of generic tones, the indicator communicates what has occurred and why, allowing traders to understand market events without relying solely on visual observation. This approach is especially valuable for visually impaired traders, but it also benefits busy or multitasking users who prefer hands-free interaction.
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CSV Data Analysis (Part 7): Statistical Robustness Testing on MQL5 CSV Exports with Monte Carlo Simulation

CSV Data Analysis (Part 7): Statistical Robustness Testing on MQL5 CSV Exports with Monte Carlo Simulation

A statistically significant backtest is not proof of a robust edge. This article presents a three-part validation battery in Python that consumes an MQL5 trade-level CSV export. A sign-randomization permutation test evaluates whether the Sortino reflects real directional skill, bootstrap BCa intervals assess metric stability, and Monte Carlo trade-order shuffling tests sequence dependence of drawdowns. The results feed a five-condition framework for deployment decisions.
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MQL5 Wizard Techniques you should know (Part 29): Continuation on Learning Rates with MLPs

MQL5 Wizard Techniques you should know (Part 29): Continuation on Learning Rates with MLPs

We wrap up our look at learning rate sensitivity to the performance of Expert Advisors by primarily examining the Adaptive Learning Rates. These learning rates aim to be customized for each parameter in a layer during the training process and so we assess potential benefits vs the expected performance toll.
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Master the Z-Score: Building Mean-Reverting MQL5 Trading Systems

Master the Z-Score: Building Mean-Reverting MQL5 Trading Systems

This article explains how to use the Z-Score to quantify price deviations in standard deviations and apply the concept in MQL5. We cover the calculation, interpretation across market regimes, and the implementation of a custom indicator and three trading strategies as Expert Advisors. Readers get complete code examples and a testing workflow, plus practical notes on lookback selection, fat tails, execution timing, and risk controls.
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CSV Data Analysis (Part 5): Real-Time CSV Streaming from Live MetaTrader 5 Sessions

CSV Data Analysis (Part 5): Real-Time CSV Streaming from Live MetaTrader 5 Sessions

This article describes a live data export framework for MetaTrader 5 built around a decoupled, three‑layer design. The MQL5 component batches bar and tick records via a write buffer and rotates CSV files daily; a Python daemon tails the stream, renders a live dashboard, and flags anomaly thresholds. The demo indicator illustrates integration points, enabling real‑time monitoring and auditability during trading sessions.
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MQL5 Wizard Techniques you should know (Part 92): Using B-Tree Indexing and a Bayesian NN in a Custom Signal Class

MQL5 Wizard Techniques you should know (Part 92): Using B-Tree Indexing and a Bayesian NN in a Custom Signal Class

In this article we present yet another custom MQL5 Signal Class that we are labelling ‘CSignalBTreeBayesian’. We are marrying the algorithm of a balanced tree with a neural network that is built on Bayesian principles to formulate yet another custom signal testable independently or with other signals thanks to the MQL5 Wizard.
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Online Linear Regression with Recursive Least Squares in MQL5: A Parameter-Free Adaptive Trend Estimator

Online Linear Regression with Recursive Least Squares in MQL5: A Parameter-Free Adaptive Trend Estimator

This article implements recursive least squares in native MQL5 with a constant O(1) update per bar, avoiding the per‑bar O(n) rebuild of a rolling OLS. It derives and codes the Sherman–Morrison rank‑1 update, explains the forgetting factor through its effective window, and provides a reusable class. Two coordinated indicators plot a 1‑step‑ahead price forecast on the chart and the signed slope in a correctly scaled subwindow for practical trend tracking.
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MQL5 Wizard Techniques you should know (Part 95): Using Disjoint Set Union and Deep Belief Network in a Custom Signal Class

MQL5 Wizard Techniques you should know (Part 95): Using Disjoint Set Union and Deep Belief Network in a Custom Signal Class

For this article we switch to a custom MQL5 Wizard class that examines entry Signals. Our custom class is ‘CSignalDSUDBN’ this time around, and is coded by combining the Disjoint Set Union algorithm with a Deep Belief network. As has been the case throughout these series, our model is testable with MQL5 Wizard-Assembled Expert Advisors that can be tuned with different trailing stops and money management classes.
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Developing a Replay System (Part 56): Adapting the Modules

Developing a Replay System (Part 56): Adapting the Modules

Although the modules already interact with each other properly, an error occurs when trying to use the mouse pointer in the replay service. We need to fix this before moving on to the next step. Additionally, we will fix an issue in the mouse indicator code. So this version will be finally stable and properly polished.
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Competitive Learning Algorithm (CLA)

Competitive Learning Algorithm (CLA)

The article presents the Competitive Learning Algorithm (CLA), a new metaheuristic optimization method based on simulating the educational process. The algorithm organizes the population of solutions into classes with students and teachers, where agents learn through three mechanisms: following the best in the class, using personal experience, and sharing knowledge between classes.
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MQL5 Wizard Techniques you should know (Part 93): Using Suffix Automation and an Auto Encoder in a Custom Money Management Class

MQL5 Wizard Techniques you should know (Part 93): Using Suffix Automation and an Auto Encoder in a Custom Money Management Class

For this article we switch to a custom MQL5 Wizard class implementation that explores Money Management. We are labelling our custom class ‘CMoneySuffixAE’ that we derive by combining the Suffix Automaton algorithm with an Autoencoder neural network. As always, this formulation is testable with MQL5 Wizard Assembled Expert Advisors that can be tuned with various entry signals and trailing stop approaches.
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Building an Adaptive Fibonacci Volatility Band Indicator in MQL5

Building an Adaptive Fibonacci Volatility Band Indicator in MQL5

We build an adaptive Fibonacci volatility band indicator in MQL5 that centers on a smoothed price (SMMA) and scales band width with a smoothed ATR. The article covers inputs, buffer mapping, ATR handling, and SMMA formulas, then projects configurable Fibonacci ratios with filled zones. Readers get a ready workflow for visualizing volatility expansion/contraction and outlining dynamic support and resistance.
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CSV Data Analysis (Part 2): Building a Production-Grade CSV Export and Parsing Pipeline for Quantitative Strategy Analysis

CSV Data Analysis (Part 2): Building a Production-Grade CSV Export and Parsing Pipeline for Quantitative Strategy Analysis

MQL5's file system operates within a strict sandbox. Understanding its access flags and path resolution rules is the foundation of any reliable export pipeline. This article builds a CCSVExporter class that handles file creation, safe appending, and error recovery. It also covers CSV parsing, field tokenization, concurrent access conflicts, and write-buffering strategies for high-frequency optimization runs.
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Extreme Value Theory in MQL5: Building a Tail-Risk Crash Gauge Beyond Monte Carlo VaR

Extreme Value Theory in MQL5: Building a Tail-Risk Crash Gauge Beyond Monte Carlo VaR

Standard MQL5 risk tools read risk from recent history and miss how heavy the downside tail can be. We implement Extreme Value Theory in MetaTrader 5: a Peaks‑Over‑Threshold fit of the Generalized Pareto Distribution via ALGLIB, a live indicator that reports EVT VaR/ES and tail shape, and an EA that sizes positions from the tail estimate. A controlled backtest illustrates reduced drawdown for unchanged entries.
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Quantum Neural Network in MQL5 (Part I): Creating the Include File

Quantum Neural Network in MQL5 (Part I): Creating the Include File

The article presents a new approach to creating trading systems based on quantum principles and artificial intelligence. The author describes the development of a unique neural network that goes beyond classical machine learning by combining quantum mechanics with modern AI architectures.
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Implementing a Continuous LLM Adaptation System for Algorithmic Trading

Implementing a Continuous LLM Adaptation System for Algorithmic Trading

SEAL (Self-Evolving Adaptive Learning) is a system for the continuous adaptation of large language models (LLMs) for algorithmic trading, designed to address the problem of rapid model degradation in changing markets. Instead of periodic retraining, which takes hours and erases old patterns, SEAL learns from every closed trade, maintains priority memory for important examples, and automatically initiates incremental fine-tuning when accuracy drops or a market regime change occurs.