Articles on data analysis and statistics in MQL5

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.

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.

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.

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.

This article builds a trend-following Expert Advisor that trades momentum spillover across markets, implemented fully in MQL5 without external solvers. It detects leaders with Derivative Dynamic Time Warping, learns a sparse weighted network by convex optimization, and propagates momentum through it with a reverting response. Readers get a step-by-step, reproducible pipeline and a working EA ready to run in the Strategy Tester.

The article describes the practical implementation of a hybrid algorithmic trading system that combines quantum computing (IBM Qiskit) and gradient boosting (CatBoost) to predict movements in the EURUSD pair on the hourly time frame. The system extracts four unique quantum features from a probability distribution across 256 states using eight qubits and, in combination with classical indicators and delta encoding of time categories, achieves 62% accuracy on 15,000 candlesticks.

We build the Matrix Profile for MQL5 from the ground up and keep it numerically stable on real prices. The library includes rolling statistics, a radix-2 FFT powering MASS, and a STOMP self-join, with results matched to stumpy. A compact facade, an indicator that draws the profile and flags discords, and a demonstration Expert Advisor show how to read and use the signal in practice.

A practical bridge from the options market into MetaTrader 5 for gold. We compute near-the-money implied volatility by solving Black-Scholes from quoted prices, compare it with 30-day realized volatility, and use the ratio as a regime proxy. A Python feed publishes the value, an MQL5 script consumes it with WebRequest, and a background service keeps a panel current and alerts on changes. Source code for all parts is provided.

MQL5 lacks native unit testing, so utility bugs in lot sizing, pip value, and normalization often slip into production. This article presents a zero‑dependency framework built from preprocessor assertion macros, interface‑based suites, and a central runner/formatter. It runs as a script in OnStart, executes deterministic tests, and prints pass/fail summaries to the Experts tab to catch rounding, boundary, and error-handling defects before deployment.

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.