Articles on data analysis and statistics in MQL5
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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Butterfly Optimization Algorithm (BOA)
The article discusses the Butterfly Optimization Algorithm, which is based on modeling foraging using the sense of smell. We will analyze the original formulas, identify and correct errors in motion equations, add a mechanism for maintaining population diversity, and present the test results.
Measuring What Matters (Part 4): Reading the Spectrum — What Eigenvalues Tell You About Risk
We turn eigenvalues from a covariance matrix into a normalized spectral‑entropy score that measures how evenly variance is spread across factors. SpectralEntropyCalculator.mq5 compares two portfolios in one run, using native vector summation, ArraySort()-based ordering, element‑wise division, and the Shannon entropy formula. The report makes dominant factors visible and enables quick, repeatable checks of diversification quality.
Expectancy and Trade Quality Score Dashboard in MQL5
We present an MQL5 script that converts closed trade history into comparable metrics: expectancy in currency, pips, and R-multiples, plus a sample-aware win rate via the Wilson interval. These inputs form a conservative, dimensionless Trade Quality Score. The tool draws a CCanvas panel, prints an Experts-tab report, and supports an hour-based session filter to analyze a defined trading window alongside full-history results.
Defining your Edge (Part 4): Applying Isotonic Regression and PNN Price-Forecasting in an Expert Advisor
We consider the methods with which Isotonic Regression calibrates raw RSI, Stochastic and price-action signal scores into probabilities that are sorted, while a separate Probability based Neural Network evaluates similar historical market states. This article uses both approaches in a ready-made MQL5 custom signal class that is compatible with MQL5 Wizard and provides up to 7 selectable entry modes. Reproducible tests compare isotonic-only signals with the combined Isotonic-PNN model to assess whether the network adds useful information beyond the simpler baseline.
Market Simulation: Position View (XVI)
In this article, we will make the necessary changes so that the position indicator displays the financial result. This way, the trader will be able to get an idea of the financial result of an open position. In addition, I will tell you something that many people do not know, even those who have been using MQL5 for a long time: how to use static variables to share memory and avoid declaring a global variable in the main code.
Enhanced Colliding Bodies Optimization (ECBO)
The article discusses the Colliding Bodies Optimization (CBO) algorithm, which is based on the physics of one-dimensional collisions between bodies. The basic version of the algorithm does not include any configurable parameters, which makes it simple. Therefore, the enhanced ECBO version — supplemented with Colliding Memory and a crossover mechanism — was used as the basis for the implementation, allowing the algorithm to achieve respectable results and earn a place in the ranking table.
Market Simulation: Position View (XV)
In this article, I will try to explain as simply as possible how messaging between applications can be used. The goal is to enable you to create something workable in the simplest and most efficient way possible whenever you can. I am not sure if I will be able to convey the idea behind this concept, since it is not that easy to understand for someone encountering it for the first time. In addition, I will take this opportunity to show you how to modify the replay/simulation system so you can debug an Expert Advisor or any other code you are developing. And all of this is just as simple and straightforward.
Honest Backtesting of Swing Strategies on Index CFDs: Financing Costs, Swap Modes, and What the Strategy Tester Cannot Model
Financing drives multi‑day index‑CFD results: in one full‑history test, swap consumed 44% of gross profit and all profit on one symbol. We convert swaps to annualized rates, contrast four brokers and two financing models with a read‑only script, and quantify a Strategy Tester issue where a single current swap is used for all history, inflating implied rates by up to seven times. The piece provides a repeatable cost‑audit method.
How to Create and Adapt an RL Agent with an LLM and Quantum Encoding for Algorithmic Trading in MQL5
The article proposes a hybrid approach to algorithmic trading based on quantum encoding of market states, Double DQN with a prioritized experience replay buffer, and an LLM acting as a contextual EA. The SEAL methodology enables asynchronous continued training of the agent without halting trading. A lightweight Q-learning filter (USE/SKIP/REDUCE) controls signal execution at the meta-level. Practical details are provided on integrating the system with the MetaTrader 5 trading platform, along with a scheme for adapting it to market regime shifts.
Market Simulation: Position View (VI)
In this article, we will implement a number of improvements to ensure that the position indicator accurately reflects the actual state on the trading server in terms of open positions and their current state. I should point out that the applications shown here are in no way intended to replace any of the elements available in MetaTrader 5. They should also not be used without due caution and a balanced approach, since their purpose is to provide educational code—that is, code intended solely for learning how the system works. The reason I call this code “educational” is that, in some cases, using messages is not the best way to implement certain functions.
The MQL5 Standard Library Explorer (Part 15): Building a Market-Regime Classifier with dataanalysis.mqh
This part focuses on practical data analysis in MQL5 with dataanalysis.mqh. We prepare a labeled dataset from bars, apply normalization, explore redundancy with PCA, and train a decision forest to classify future bar regimes. The article shows how to obtain out-of-bag estimates and permutation importance, helping you validate the model and understand which inputs matter most.
Cricket Algorithm (CA)
The article discusses the Cricket Algorithm, a metaheuristic optimization method that combines elements of the Bat Algorithm and the Firefly Algorithm with the physical laws governing the propagation of sound in the atmosphere. The algorithm simulates the behavior of crickets that navigate by the chirping of their conspecifics, using Dolbear's law and acoustic formulas to guide the search for best solutions.
Adaptive Position Sizing in MQL5: A Prototype Risk Engine with Generalized Kelly and Bootstrap Calibration
This article presents a modular position sizing engine for MetaTrader 5 that operates on normalized R-multiples. A layered pipeline combines enriched trade statistics, a generalized Kelly edge estimate, volatility-aware adjustment, Monte Carlo calibration under ruin and drawdown limits, a continuous risk policy, an exposure guard, and a broker-aware lot calculator. The output is a broker-valid lot size with an optional CSV audit trail, providing a transparent prototype for implementing modern risk controls in native MQL5.
Working with ONNX Models in MQL5 (Part 1): Decoding the Model File with a Protobuf Parser
We decode ONNX files in pure MQL5 by implementing a Protocol Buffers reader from scratch. We generate a sample network in Python, verify it in Netron, and then parse the same binary to recover graph nodes, connections, weight tensors, and input/output shapes. The result is a MetaTrader 5 program that inspects a trained model's structure before inference, without any external libraries.
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.
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.
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.
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.
Market Simulation: Position View (XIII)
In this article, we will look at how to easily implement an indicator that shows whether a position is generating a profit or a loss. The procedure is simple and effective. Even without in-depth expertise, this indicator will allow you to easily recognize when to close a position. This way, you will avoid unexpected results, since the calculation reflects the actual outcome you would get if you closed the position.
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.
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.
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.
Combining 3D Bars, Quantum Computing, and Machine Learning into a Unified Trading System
The article presents the full integration of the 3D-bar module into a quantum-enhanced trading system for forecasting the movement of currency pairs. The system combines stationary four-dimensional features, an 8-qubit quantum encoder, and CatBoost gradient boosting with 52+ features. The system is implemented in Python using MetaTrader 5, Qiskit, CatBoost, and optional integration with the Llama 3.2 LLM for interpreting forecasts.
Market Simulation: Position View (XII)
In this article, you will learn how to create a visual signal on your trading platform so you can determine directly on the chart whether a position is long or short, without having to open the Terminal. In addition, the article also explains how to implement a feature that improves the display when moving Take Profit and Stop Loss lines by hiding the horizontal line that follows the mouse cursor while these lines are being moved, to avoid confusion. The article provides practical insight into setting up market simulation systems.
Ecological Cycle Optimizer (ECO)
The ECO (Ecological Cycle Optimizer) algorithm offers an interesting metaphor for applying the concept of the ecological cycle to the field of metaheuristic optimization. The idea of dividing a population into trophic levels — producers, herbivores, carnivores, omnivores, and decomposers — creates a hierarchical search structure, in which each group contributes to the overall optimization process.
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.
Machine Learning Under Constraint (Part 1): A Configurable Rule Set for Prop-Firm Position Sizing
Hardcoded prop-firm rules lock the sizer to one program. This article factors those rules into a PropFirmRuleSet and refactors PropFirmAccountState and the sizing modifiers to consume it, including dynamic versus fixed daily limits and the news-window profit-credit haircut. Parity against the original FundedNext behavior is validated on a simulated equity path, so you can retarget sizing by configuration instead of rewriting code.
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.
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.
Market Simulation: Position View (IX)
In this turning-point article, we will begin to explore in greater depth the interaction between the applications we are developing to ensure full support for the replay/simulation system. Here we will analyze a problem that, on the one hand, is quite unpleasant, but on the other hand, is very interesting to explain and solve. The problem is this: how can we restore the take-profit and stop-loss lines after they have been deleted, and do so without using the terminal by performing the operation directly on the chart? At first glance, it seems simple. However, there are several obstacles that must be overcome.
Markov Chain Monte Carlo Sampling Methods: The HMC Algorithm
The article examines the Hamiltonian Monte Carlo (HMC) algorithm — the gold standard for sampling from complex multivariate distributions. A full-featured implementation of HMC in MQL5 is presented, including adaptive mass matrix tuning, MAP estimation using the L-BFGS optimization method, and comprehensive diagnostics.
Market Simulation: Position View (VIII)
In the previous article, we considered how to implement a position indicator that allows you to close an open position directly from the chart by interacting with an object available on the chart. After completing and testing the first mechanism, we began making changes to ensure that take-profit and stop-loss levels could be removed for an open position. However, since the necessary changes required detailed explanations, in that same article I showed only the changes that needed to be made to the expert advisor; I still needed to show the changes that needed to be made to the position indicator.
Survival Analysis for Trade Exits: A Discrete-Time Competing-Risks Model in MQL5
Fixed exits ignore state changes while a trade is open. We implement a discrete-time competing-risks model entirely in MQL5, estimate cause-specific hazards for take-profit and stop-loss via Newton–Raphson on a person-period dataset with time-varying features, and turn cumulative incidence into a bar-by-bar hold-or-close rule, then test it against fixed take-profit/stop-loss with identical entry logic.
Dandelion Optimizer (DO)
The Dandelion Optimizer (DO) turns the simple flight of a seed carried by the wind into a mathematical search strategy. The three phases — vortex rising, drift toward the center of the population, and landing along a Lévy-flight trajectory — form an elegant metaphor that yields interesting results in practice.
Market Simulation: Position View (VII)
In this article, we'll start making some improvements to the position indicator so that we can interact with it and modify price lines or close a position directly through the position indicator. Before we move on to the implementation, there are a few things worth clarifying, especially for those who aren't familiar with this. The indicator cannot be used in any way to change anything on the trading server. This is because MetaTrader 5 has a security system in place that allows only Expert Advisors to modify orders and positions. No application other than an Expert Advisor can manipulate orders or positions.
Combining LLM, CatBoost, and Quantum Computing into a Unified Trading System
The article proposes a synthesis of new technologies to overcome the limitations of classical indicators in market data analytics. It shows how language models and quantum encoding can reveal hidden market patterns that traditional methods overlook. The experiment confirms the value of new technologies and proposes an updated analysis methodology aligned with the current state of computational innovation.
Price Action Analysis Toolkit Development (Part 80): Building a History Navigator for MetaTrader 5
We implement a History Navigator for MetaTrader 5 that jumps the chart to an exact historical period by date and time. The dialog validates inputs, converts them to datetime, and searches bar times with a binary-search routine before centering the selected candle. The navigation logic is separated from chart control, improving testability and maintenance, and a one-click return restores the live market view.
Dendritic Cell Algorithm (DCA)
The Dendritic Cell Algorithm (DCA) is a metaheuristic inspired by the mechanisms of the innate immune system. Dendritic cells patrol the search space, accumulate signals about the quality of positions, and reach a collective decision: whether to exploit what they have found or to continue exploration. Let's take a look at how a biological model for detecting pathogens is transformed into an optimization algorithm.
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.
Deterministic Dendritic Cell Algorithm (dDCA)
The article presents an adaptation of the Deterministic Dendritic Cell Algorithm (dDCA) for continuous optimization problems. The algorithm, inspired by the immune system's Danger Theory, uses a signal accumulation mechanism to automatically balance exploration and exploitation within the search space.