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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Hypothesis Testing for Trading Strategies — Proving Whether Your Edge is Real

Hypothesis Testing for Trading Strategies — Proving Whether Your Edge is Real

Net profit and win rate do not tell you if a strategy's edge is statistically real. This MQL5 toolkit analyzes return series built from price data or deal history and reports t‑statistics, p‑values, and confidence intervals using one-sample and Welch t‑tests, the Mann–Whitney U test, and volatility‑regime analysis to support evidence‑based trading decisions.
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Market Simulation: Position View (X)

Market Simulation: Position View (X)

We need a way to handle the graphical objects we create. The approach presented in the previous article works very well for certain scenarios. In this case, we will need something more complex, given the specific nature of the problem at hand. Therefore, we will not attempt to replace the ZOrder management mechanisms already present in MetaTrader 5, nor, of course, will we check which object is in the foreground or covered by another object. We are going to do something completely different. Here, I will show you what changes need to be made to the code in order to use part of what MetaTrader 5 already does for us.
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Bidirectional LSTM and Quantum Computing for Predicting the Direction of Price Movement

Bidirectional LSTM and Quantum Computing for Predicting the Direction of Price Movement

The article presents a reproducible implementation of a hybrid quantum-neural network model for algorithmic trading on Forex without using real quantum hardware. A fixed three-qubit quantum circuit in IBM Qiskit converts sliding-window statistics (mean returns, volatility, and range) into a probability distribution, from which seven quantum metrics are calculated. These features are integrated into a bidirectional LSTM architecture with regularization and mechanisms to address class imbalance, including focal loss and a sampler.
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Isolation Forest: Unsupervised Anomaly Detection, and What It Actually Finds in Price Data

Isolation Forest: Unsupervised Anomaly Detection, and What It Actually Finds in Price Data

This article implements a self-contained Isolation Forest library for MetaTrader 5 with no labels, no distribution assumptions and no external dependencies. It details a reproducible 64‑bit generator, tree/forest construction, scoring and feature design, then verifies results against Python and market data with two null models. The package includes an indicator that plots the decision variable and a gate example. Readers get a validated library, clear limits of applicability and a practical way to calibrate thresholds.
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Defining your Edge (Part 3): Using HMM and GRU in an Expert Advisor

Defining your Edge (Part 3): Using HMM and GRU in an Expert Advisor

We examine how a Hidden Markov Model (HMM) estimates latent market regimes while basing on observable price and indicator sequences. This is done by estimating the probability of state transitions. A Gated Recurrent Unit (GRU) network models time dependencies and keeps important information over several observations. In an Expert Advisor, HMM-based regime probabilities, can be merged with GRU-based sequence learning to better classify increments in accumulation, distribution, and momentum prior to their showing up in regular price confirmations.
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CSV Data Analysis (Part 8): Building an SQLite Strategy Registry from Accumulated CSV Exports

CSV Data Analysis (Part 8): Building an SQLite Strategy Registry from Accumulated CSV Exports

Flat files work well at the start of an MQL5 research pipeline, but they hinder cross-run queries and provenance once the archive grows. We build a Python-based SQLite registry that ingests CSV exports with SHA-1 deduplication, records EA version and run timestamps, applies forward-only schema migrations, and indexes common filters. You get a structured query layer for fast lookups, robustness checks, and version comparisons across all campaigns.
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Price Action Analysis Toolkit Development (Part 81): Adding Persistent Historical Bookmarks to an MQL5 Navigator

Price Action Analysis Toolkit Development (Part 81): Adding Persistent Historical Bookmarks to an MQL5 Navigator

We introduce a persistent bookmark layer for the MetaTrader 5 History Navigator. Bookmarks capture a chart's symbol, timeframe, and historical position with a name and notes, write them to a CSV file, and reload them later without manual date entry. The implementation integrates bookmark management into the current navigation engine, enabling quick creation, selection, navigation, and deletion for efficient historical study.
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Market Simulation: Position View (XI)

Market Simulation: Position View (XI)

In this article, I will show you, dear reader, how to select the objects we create on the chart and modify the position indicator so that it can perform many more functions than originally intended. We will look at how to implement the ability to move price levels and create price lines directly on the chart. Many people may find this difficult. However, you will see that we'll do this with minimal effort. You just need to give it a little thought.
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Market Simulation: Position View (XIV)

Market Simulation: Position View (XIV)

Now we will implement this solution, since MQL5 is based on the same principles as event-driven programmingю Developers often use this model when creating DLLs. I know that at first, the event-driven model will seem confusing and illogical. But in this article, I will explain the principles of event-driven programming in a way that is easier to understand, so that if you are just getting started, you will have a clear grasp of how it works. Understanding what I am about to explain in this article will help you throughout your work as a programmer.
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Partial Information Decomposition: When Two Indicators Together Say More Than Either Alone

Partial Information Decomposition: When Two Indicators Together Say More Than Either Alone

We introduce a Partial Information Decomposition library for MQL5 that decomposes two sources about a target into four atoms: unique to each, shared, and synergy. The implementation uses quantile binning, tabulated logarithms, and a maximum-entropy fit (for I_ccs), and it pairs results with a block-permutation null because atoms sit above zero on finite samples. Use it to screen indicator pairs and judge significance, including family-wise correction.
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Eco-inspired Evolutionary Algorithm (ECO)

Eco-inspired Evolutionary Algorithm (ECO)

The article discusses the ECO optimization algorithm, which is based on ecological concepts: populations are grouped into habitats based on territorial proximity, exchange genetic material within habitats, and migrate between them. Despite its wide range of operators and elegant biological metaphor, the algorithm produced a certain result discussed below.
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Ebola Optimization Search Algorithm (EOSA)

Ebola Optimization Search Algorithm (EOSA)

The article examines the EOSA algorithm, which is inspired by the mechanisms of Ebola virus transmission: short-distance transmission through close contact (exploitation) and long-distance transmission through travel (exploration). An analysis of the original publication revealed critical issues in the mathematical formulas and an epidemiological model that was impractical to implement, which required a significant overhaul of the algorithm to produce a workable implementation.
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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.