Articles on data analysis and statistics in MQL5

This article presents a compact MQL5 library for market-complexity analysis: LZ76 complexity and Normalized Compression Distance built on a SAX symbolizer, exposed through a simple facade and an efficiency indicator. It explains the discretization choices, normalization, and distance formulation, and validates the code with unit checks and an independent cross-check. You get a ready-to-use library and indicator, plus a disciplined way to interpret readings with a shuffle null and a direction check.

Aggregate metrics alone do not reveal how a trade sequence manages risk. This MQL5 tool analyzes closed positions to flag four structural patterns: post-loss volume escalation, overlapping same-direction entries, asymmetric payoffs, and a classical risk-of-ruin figure. The results are merged into a configurable A-F grade with concise recommendations to guide further review.

The article discusses the Differential Search Algorithm (DSA), which simulates the migration of a superorganism in search of optimal living conditions. The algorithm uses a Gamma distribution to generate a pseudo-stable random walk and offers four strategies for selecting the direction of movement, along with three coordinate mutation mechanisms. How will this method perform?

We complete the native MQL5 port of Kronos: the decoder, the predictor's decode_s1 and decode_s2 stages with their cross-attention traps, and the autoregressive loop that produces a multi-bar forecast. Then we profile and make it roughly 4.5x faster with an exact KV-cache and pre-transposed weights, verifying every stage against PyTorch.

Trend-scanning supports both forward and backward windows, and the labeling default is unsafe for features: it looks ahead and boosts next-bar agreement well above chance on random walks. We provide a dedicated wrapper, get trend scanning features, that forces computational causal and returns only window, slope, t value, and rsquared. A second analysis quantifies errors introduced by the default log transform on signed series.

The article shows how to evaluate machine-learning alphas before a full backtest by expressing them as formulaic alphas. We compute Information Coefficient (IC), Rank IC, Information Ratio (ICIR), and t-statistics to quantify forecasting strength and stability. A MetaTrader 5 backtest illustrates differences versus execution-dependent tests, and a Python parser facilitates reproducible calculations and bulk screening.

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.

An innovative indicator based on prime number theory helps identify strong reversal levels that other traders overlook. Testing on 10 assets showed that reversals in mathematically significant zones occur 1.5 to 1.8 times more frequently. Five practical application scenarios with specific rules for filtering out false breakouts and making precise market entries.

This article builds a Kolmogorov–Arnold Network (KAN) in MQL5, where every edge carries a learnable B‑spline curve rather than a scalar weight. We construct the spline basis, assemble edges and a layer, and fit all coefficients by ridge‑regularized least‑squares in a single solve. The model is delivered as an indicator that visualizes the learned curves and an Expert Advisor that acts on the prediction, providing an interpretable, reusable codebase.

EGARCH models log-variance, avoiding the non-negativity constraints that can distort GARCH estimates and enabling a clear treatment of leverage asymmetry. The article provides a complete MQL5 implementation with logarithmic backcasting, simulation-based multi-step forecasting, and diagnostics including the Engle–Ng Sign Bias, Leverage Correlation, and Volatility Runs tests. Practical outputs include EGARCH Volatility, an Innovation Z-Score, and an Asymmetric Volatility Regime Oscillator to support regime analysis and strategy design.

Experimental evaluation on standard benchmark functions reveals the advantages and limitations of directly adapting combinatorial algorithms. The article provides a detailed description of the ECEA algorithm's mechanisms and test results.

This article performs a numerical verification of MQL5 eigendecomposition for a covariance matrix using the spectral theorem A = V Λ Vᵀ. It reconstructs the matrix with Diag(), Transpose(), and MatMul(), computes the residual and its Frobenius norm, and shows that deviations remain at floating‑point precision, with results printed to the Experts journal.

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 article provides a practical research setup for weekend gap analysis: MQL5 extracts precise pip‑based gaps and tracks fills, while Python performs statistical testing and visualization. You will compute fill rates by gap buckets, model fill probability with logistic regression, and assess time-to-fill via Kaplan–Meier curves. All steps are configurable and reproducible for EURUSD, GBPUSD, USDJPY and beyond.

We implement a Future Swing Projection indicator in MQL5 that analyzes historical swing structure and estimates the next move from recent price behavior. It locates six alternating swing points, measures five completed legs, and uses their average distance to project a target five bars ahead. The indicator draws swing legs, a projection line, ATR‑based support and resistance zones, and a label with the projected price to keep the process rule‑based and reproducible.

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.

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.