Articles on data analysis and statistics in MQL5

Biogeography-Based Optimization (BBO) is an elegant global optimization method inspired by natural processes of species migration between islands within archipelagos. The algorithm is based on a simple yet powerful idea: high-quality solutions actively share their characteristics, while low-quality ones actively adopt new features, creating a natural flow of information from the best solutions to the worst. A unique adaptive mutation operator provides an excellent balance between exploration and exploitation. BBO demonstrates high efficiency on a variety of tasks.

Learn a practical way to execute MetaTrader 5 trades from Telegram voice notes using a Python middleware and an MQL5 EA acting as an HTTP client. The article covers architecture, WebRequest polling, in-memory queuing, JSON parsing with null-terminator stripping, and a constrained command grammar with a 0.001-lot default. You will configure the environment and validate round‑trip latency suitable for mobile data connections.

Learn how to create an EX5 module of exportable functions that seamlessly query and save data for the most recently filled pending order. In this comprehensive step-by-step guide, we will enhance the History Management EX5 library by developing dedicated and compartmentalized functions to retrieve essential properties of the last filled pending order. These properties include the order type, setup time, execution time, filling type, and other critical details necessary for effective pending orders trade history management and analysis.

The article considers the classification model of Gaussian processes. We will start by studying its theoretical principles moving on to the practical development of the GP library in MQL5.

Symbolic Aggregate approXimation (SAX) encodes price windows as short words to enable fast, sound similarity search on history. We implement SAX in pure MQL5, including Gaussian breakpoints, PAA, and the lower-bounding MINDIST, and validate it with a test harness. An indicator applies a no-lookahead, two-stage search, summarizes forward paths in ATR units, and draws a forecast fan, explicitly indicating when the sample shows no edge.

Kohonen's self-organizing maps transform the chaos of market data into an ordered two-dimensional map, where similar patterns are grouped together. The article demonstrates a complete implementation of a SOM in an MQL5 Expert Advisor with 400 neurons and continuous learning. We break down the Best Matching Unit search algorithm, weight updates using a Gaussian neighborhood function, integration with quantum effects, and the generation of trading signals. The code is open-source, the math is clear, and the results are verifiable.

We resume the topic of optimization by the scientific community. CoSO should not be viewed as a ready-made solution, but as a promising research platform. With proper development, CoSO can find its niche in tasks where adaptability and resilience to change are important, and computation time is not critical.

The article presents a new approach to solving optimization problems by combining ideas from bacterial foraging optimization (BFO) algorithms and techniques used in the genetic algorithm (GA) into a hybrid BFO-GA algorithm. It uses bacterial swarming to globally search for an optimal solution and genetic operators to refine local optima. Unlike the original BFO, bacteria can now mutate and inherit genes.

We have been working on just the indicators for a long time now, but now it's time to get the service working again and see how the chart is built based on the data provided. However, since the whole thing is not that simple, we will have to be attentive to understand what awaits us ahead.

We replace native MetaTrader chart objects with a canvas-based drawing engine that renders tools pixel-by-pixel on a full-chart bitmap layer. The article implements persistent object storage with per-tool style memory, precise hit testing, selection, whole-object dragging, and handle manipulation. It also adds new line tools, a reorganized category system with a one-click delete action, and a rubber-band preview for multi-click placement.

In this article we present the implementation of a feature selection algorithm described in an academic paper titled,"FREL: A stable feature selection algorithm", called Feature weighting as regularized energy based learning.

The main purpose of this article is to introduce and explain the C_ChartFloatingRAD class. We have a Chart Trade indicator that works in a rather interesting way. As you may have noticed, we still have a fairly small number of objects on the chart, and yet we get the expected functionality. The values present in the indicator can be edited. The question is, how is this possible? This article will start to make things clearer.

Building on the partition function analysis from Part 1, this article deepens the theoretical foundation before completing the analytical pipeline. We first give a full treatment of the Hurst exponent: what it measures, what it implies about market memory, and why it matters for the MMAR. This is followed by an intuitive exploration of multifractal spectra and what f(α) reveals about volatility heterogeneity. We then move to implementation: extracting the scaling function τ(q), estimating H via R/S analysis, and fitting the multifractal spectrum across four candidate distributions. By the end, we have the complete parameter set needed to construct the MMAR process in Part 3. Part 2 of an eight-part series.

The article delves into the implementation of a modified Forward Selection Component Analysis algorithm, drawing inspiration from the research presented in “Forward Selection Component Analysis: Algorithms and Applications” by Luca Puggini and Sean McLoone.

The article presents a new metaheuristic method based on the hunting strategies of Australian dingoes: group attack, chase, and scavenging. Let's see how the Dingo Optimization Algorithm (DOA) performs algorithmically.

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.

This article starts the MMAR pipeline on EURUSD M5 data. We load market data via the MetaTrader5 Python API and run partition-function analysis with non-overlapping intervals to test for multifractal scaling. The result is an evidence-based decision on fractality, a prerequisite for building MMAR and for choosing whether to proceed beyond GARCH.

The article builds a reusable validation layer for Expert Advisors in MQL5. It implements lot-size rules and normalization, SL/TP and freeze-level guards, price digit normalization, margin sufficiency checks, unchanged-level filtering on modifications, account order-limit control, new-bar detection, symbol tradability checks, economic-calendar news windows, and session detectors. The result is cleaner code and fewer terminal errors in live trading.

A revolutionary approach to machine learning in trading through quantum computing. The article demonstrates a practical implementation of an adaptive QRC system with continuous retraining for predicting market movements in real time.

This article builds a white-box classifier in MQL5 using the Tsetlin Machine. It learns human-readable AND-rules instead of weights, trains with integer state updates, and requires no external dependencies. You will assemble the automaton, clause, and multi-class voter, verify on XOR and other boolean tasks, booleanize indicators, label by forward ATR-scaled return, save the model to CSV, and view active rules on a live chart.

The second part of the series examines the mathematical framework for multivariate random variables, which is necessary for analyzing the dependence and joint behavior of market assets. This section describes joint distribution functions, the concepts of marginal and conditional distributions, and the conditions for dependence and independence of variables. The theoretical material is based on extending the analogy between probability and mass to multidimensional space. Particular attention is given to measures of association: from classical linear covariance and correlation to modern tools such as copulas and Shannon mutual information.

We extend the canvas drawing layer from the previous part with seven new categories of multi-anchor analytical drawing tools, covering three channel variants, three pitchfork variants, three Gann tools, and the six Fibonacci tools. We work through how each tool encodes its geometry on the canvas, how derived handles let users reshape compound shapes coherently, and how shared helpers handle ray clipping, scanline filling, and anti-aliased arc rendering. By the end, we will have a full set of analytical drawing tools that live on the same interactive canvas alongside the basic line tools from the previous part.

In this article, we will implement a control indicator so that it can be integrated into the message system we are developing. Although it is not very difficult, there are some details that need to be understood about the initialization of this module. The material presented here is for educational purposes only. In no way should it be considered as an application for any purpose other than learning and mastering the concepts shown.

In this article, we introduce a modified version of stepwise feature selection, implemented in MQL5. This approach is based on the techniques outlined in Modern Data Mining Algorithms in C++ and CUDA C by Timothy Masters.

This article adds eight volatility functions to MicroStructure_Foundation.mqh, including realized volatility, duration-adjusted volatility, fractional volatility, a FIGARCH-inspired proxy, a volatility clustering index, a GJR-GARCH asymmetry measure (using the Dube library), bipower-variation jump detection, and a wrapper function. The MFDFA implementation is revised to return the conventional Legendre-transform Δα with an R² confidence field, replacing the τ-spread proxy used in the original submission. Thresholds are derived from 514 NY sessions of NQ E-mini Nasdaq 100 futures (May 2024–May 2026); no new include file is created.

We describe an MQL5 framework that aligns entries with session rhythms and scheduled clock events. A script identifies the broker's time zone and DST by detecting NFP spikes on EURUSD and matching them to EU/US/AU transition dates, producing EA‑ready settings. Session-to-broker time conversion and 15-minute marks constrain execution. A multi‑timeframe AMA signal aggregates trends for strategy selection and optimization.

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.

Before we can move forward, we need to fix a few things. These are not actually the necessary fixes but rather improvements to the way the class is managed and used. The reason is that failures occurred due to some interaction within the system. Despite attempts to find out the cause of such failures in order to eliminate them, all these attempts were unsuccessful. Some of these cases make no sense, for example, when we use pointers or recursion in C/C++, the program crashes.