Articles on data analysis and statistics in MQL5

Financial management as an ecosystem: Seven AI traders with different personalities and strategies instead of a single algorithm. They compete for capital, learn from their mistakes, and make decisions collectively. The article explains the principles behind the Modern RL Trader system, in which the code possesses consciousness and emotions, creating a living, evolving trading mind.

The article examines a Williams five‑bar fractal feature pipeline and shows how a centered rolling window creates a true look‑ahead leak. It identifies two additional silent bugs—a hardcoded shift tied to the default n and a volatility threshold that ignores its input—and consolidates fixes under a single leak_safe flag. Readers get leak‑free fractal, level, trend, and signal features, plus guidance on when unshifted columns remain valid for labeling.

This article shows how to generate a dependency-free, single-page PDF report in MQL5 using only string assembly and the FILE_BIN API. The script computes per-symbol trade statistics, then renders a labeled table and an equity curve with explicit PDF color and drawing operators. Statistics are calculated in a standalone module, so every value can be verified against synthetic data without relying on a live trading account.

Live performance often drifts from backtests because of execution friction. We introduce an MQL5 diagnostic EA that records entry and exit slippage, asymmetry, observed spread, requotes, and per-leg latency, using a precise probe mode and an approximate passive mode, and writes every sample to CSV. Use the results to distinguish strategy issues from execution effects across your terminal, network, broker, and liquidity.

The article examines slice sampling — an adaptive MCMC algorithm that automatically adjusts its sampling parameters. Its effectiveness is demonstrated using Bayesian linear and logistic regression models, and the results are compared with classical frequentist methods.

The article describes the development of a multi-agent machine learning system for algorithmic trading on MetaTrader 5 based on reinforcement learning. The system has a three-tier architecture: memory neurons store experience, agents make independent decisions, and the collective mind combines them through weighted voting. The system is continuously improved through Q-learning, pruning of ineffective neurons, and evolutionary reduction of exploration.

We build a CSV exporter for MQL5 custom indicators that preserves the exact values seen on the chart. The script creates the indicator handle with iCustom, waits for BarsCalculated, aligns buffers to CopyRates, and writes a locale-safe CSV that pandas loads with parsed dates and NaN for warm-up bars. It addresses compile-time argument limits, jagged-array workarounds, and EMPTY_VALUE handling, enabling reliable Python backtests without re-coding the indicator.

This article implements BOSS from scratch in MQL5 and applies it to regime classification: SFA turns windows into words, bags record word frequencies, and an ensemble over window lengths votes on labels. We cover the encoding steps, the BOSS distance, training with auto-generated regime labels, and practical parameters. A BTCUSD benchmark versus DTW shows higher macro accuracy on clean data and markedly faster inference.

This article presents two versions of the Crystal Structure Algorithm: the original and the modified version. The Crystal Structure Algorithm (CryStAl), published in 2021 and inspired by the physics of crystal structures, was positioned as a parameter-free metaheuristic for global optimization. However, testing revealed a critical problem with the algorithm. A modified version, CryStAlm, is also presented; it addresses the original's key shortcomings.

The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method that is widely used to approximate posterior distributions in Bayesian inference. This article describes the theoretical foundations of the algorithm, the implementation of the MHSampler class in MQL5, and examples of its application, including an analysis of the resulting samples.

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.

A metaheuristic algorithm that simulates the growth of coronary arteries in the human heart for optimization problems. It uses the principles of angiogenesis (the growth of new blood vessels), bifurcation (branching), and pruning of weak branches to find optimal solutions in a multidimensional space. Testing its effectiveness across a wide range of tasks yielded unexpected results.

The article delivers a complete, verifiable tick export path from MQL5 to a binary file and into Python. It defines a 64‑byte header, 48‑byte records with millisecond time and flags, an export pipeline using CopyTicksRange(), and a single‑call NumPy loader. Users obtain compact, precision‑preserving files and a reproducible workflow for vectorized analysis.

What if lunar cycles and seasonal patterns influence the foreign exchange markets? This article shows how to translate astrological concepts into the language of mathematics and machine learning. I built a Python system with 88 features based on astronomical cycles, trained CatBoost on 15 years of EURUSD data, and obtained some intriguing results. The code is open-source, the methods are verifiable, and the conclusions are unexpected — ancient wisdom meets gradient boosting.

We present a native MQL5 implementation of the catch22 feature set: all 22 canonical time-series characteristics in a reusable class validated against pycatch22. Using a leak-free pipeline (chronological split, purging, embargo), we run a three-arm ablation—classic indicators, catch22, and combined—for volatility-regime classification. Finally, we deploy the combined model as a Strategy Tester regime filter to quantify its impact on a simple baseline strategy.

A market-neutral trading strategy based on the empirical return distribution offers an alternative to traditional technical analysis methods, replacing price direction forecasting with the statistical placement of orders at levels the price is likely to reach. This article provides a detailed analysis of the mathematical framework for calculating percentiles, algorithms for weighting position sizes based on the probability of an order being triggered, and mechanisms for adapting to changing market conditions through grid expiration. A complete implementation in MQL5 is provided.

The Crow Search Algorithm (CSA) is an elegant metaheuristic inspired by crows’ ability to hide food and find other crows' caches, solving optimization problems by balancing following successful solutions with random exploration of the search space. Let's find out how well the algorithm performs.

Learn to assemble an MT5 Expert Advisor that hosts a chart management dashboard written in MQL5. The guide walks through shared definitions, symbol acquisition and filtering, chart lifecycle functions, and a UI panel with search, scrolling, and state indicators, all driven by events and a timer. The result is a reproducible tool that reduces clicks and accelerates multi-symbol analysis.

This article demonstrates a practical approach to researching trading ideas using a range breakout strategy as an example. We will go through the entire process, from formalizing trading rules and building a baseline model to parameter optimization, forward testing, and evaluating the robustness of the results. The main goal of the article is to develop an understanding of how statistics and testing can be used to identify, validate, and evaluate trading hypotheses.

Stop-loss and take-profit placement is usually the least-measured decision in a trading system. This Expert Advisor reads your closed history, replays M1 price between each entry and exit to measure Maximum Adverse and Favorable Excursion per trade, and splits winners from losers. From the distributions and trade efficiency it derives data-driven stop and target levels - measured from your own account, not a rule of thumb. Analysis only; it does not trade.

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.

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.

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.

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.

The article introduces the Mapper pipeline in MQL5 by implementing the two fundamental components: CTDAMapperFilter (lens) and CTDAMapperCover (overlapping intervals). It explains three lens options—eccentricity, density, and coordinate—plus cover parameters (resolution and gain), and demonstrates how a price point cloud is reduced to one value per point and interval memberships. Readers obtain ready inputs for subsequent clustering and graph construction.

The article describes an interesting approach to algorithmic trading based on symbolic mathematical equations instead of traditional machine learning "black boxes". The author demonstrates how to transform opaque neural networks into readable mathematical equations using the SymPy library and polynomial regression, allowing for a full understanding of the logic behind trading decisions. The approach combines the computational power of ML with the transparency of classical methods, giving traders the ability to analyze, adjust, and adapt models in real time.

In this article we make the case for pairing the Discrete Fourier Transform with a Spiking Neural Network in a Trading Robot. The Fourier Transform helps represent data as oscillations instead of its raw values. To govern how we interpret these cycles, we engage a Spiking Neural Network that unlike regular networks, uses time dependent electrical charges to accumulate potential and only "spike" when a target threshold is met. Combining these two engines allows us better control on the timing of discrete market movements, that in theory should give us entry signals with rigorous mathematical confirmation.

The custom modification of the Dingo algorithm presented in the article has raised the bar for finding the best optimization algorithm. Are even better results possible?