Articles on data analysis and statistics in MQL5

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.