Articles on data analysis and statistics in MQL5

In this article, we shift from Python research to native MQL5 engineering. We build the first module of the MMAR library: a shared constants header, an SVD-based OLS regression class, a Generalized Hurst Exponent estimator, and the partition analysis engine that computes the partition function, extracts tau(q), estimates H via zero-crossing interpolation, and scores multifractality through three diagnostic tests. Tested on 500,000 bars of EURUSD M10, the engine correctly classifies the data as multifractal in under four seconds. Part 4 of an eight-part series. Part 5 fits the tau(q) curve to four candidate distributions via the Legendre transform.

Batch normalization is the pre-processing of data before it is fed into a machine learning algorithm, like a neural network. This is always done while being mindful of the type of Activation to be used by the algorithm. We therefore explore the different approaches that one can take in reaping the benefits of this, with the help of a wizard assembled Expert Advisor.

We are beginning to implement the connection between Excel and MetaTrader 5, but first we need to understand some key points. This way, you won't have to rack your brains trying to figure out why something works or doesn't. And before you frown at the prospect of integrating Python and Excel, let's see how we can (to some extent) control MetaTrader 5 through Excel using xlwings. What we demonstrate here will primarily focus on educational objectives. However, don't think that we can only do what will be covered here.

In this article, we will finally solve the problems with the simulation of ticks on a one-minute bar so that they can coexist with real ticks. This will help us avoid problems in the future. The material presented here is for educational purposes only. Under no circumstances should the application be viewed for any purpose other than to learn and master the concepts presented.

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 extends MicroStructure_Foundation.mqh with a MicrostructureAnalysis struct and five functions that decompose M1 price variation into a quoted spread proxy, Roll-implied spread, OHLC-based noise ratio, order imbalance, and an adverse selection component. A wrapper populates these fields and links them to the volatility suite from Part 4. Empirical thresholds come from 602 NQ E-mini NY sessions (Jan 2024–Jun 2026), helping you gate volatility signals, size risk, and recognize spread-driven frictions.

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.

For this article we look at a custom MQL5 Wizard class for Trailing Stops. Our implemented custom class ‘CTrailingConvexHullGRU’, is built from merging the Convex Hull algorithm with a GRU network. As always we seek to develop a model that is testable with MQL5 Wizard-Assembled Expert Advisors and can be tuned with various Money Management and entry Signals classes. Our testing is with the 'Envelopes' and the RSI classes for Signal.

The article establishes a reproducible method to measure portfolio risk for multiple symbols using MQL5 matrices and OpenBLAS. It covers computing log returns, building a covariance matrix, and evaluating wᵀΣw instead of summing individual variances. A complete script prints naive versus true volatility and the cross‑term contribution, enabling you to detect when correlated instruments inflate exposure beyond single‑asset estimates.

Downloading international monetary fund data in Python: Mining IMF data for use in macroeconomic currency strategies. How can macroeconomics help an ordinary and an algorithmic trader?

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 delivers MQL5 implementations of FIGARCH and HARCH and updates the volatility library for long‑memory processes. It provides code for Hurst and GPH testing, parameter setup (truncation and horizons), and scripts for fitting, forecasting, and simulations. Readers learn how to apply and compare the models on market data to select an appropriate specification.

The article describes a competitive architecture for MetaTrader 5 in which ten LLM agents, each with different trading rules, manage their own capital and open independent positions using unique magic numbers. The system prompt and the agent's trading aggressiveness are adjusted based on PnL results and the trade streak. A reproducible framework with operating modes and monitored metrics is presented, suitable for testing and further optimization.

After a break in development and improvement of the service used for replay/simulator, we are resuming work on it. Now that we've abandoned the use of resources like terminal globals, we'll have to completely restructure some parts of it. Don't worry, this process will be explained in detail so that everyone can follow the development of our service.

The article presents a practical foundation for shape analysis of price series in MQL5. It implements Takens time‑delay embedding to build a phase‑space point cloud and computes the full pairwise distance matrix under selectable norms. The CTDAPointCloud and CTDADistance classes are provided with a demo script that embeds chart data and outputs results, preparing inputs for downstream topological tools.

A GPH‑based estimator for d, the key ARFIMA parameter, is added to MicroStructure_Foundation.mqh. GPHEstimator() computes d via log‑periodogram regression, while PopulateARFIMAAnalysis() stores d with an R² confidence score and validates the theoretical relationship H = d + 0.5. An empirical study on 72 US100 M1 sessions confirms pooled d = −0.006, consistent with the random walk boundary established in Part 2.

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.

This article presents a swing-based volume profile indicator in MQL5 that analyzes platform tick volume within completed high-to-low and low-to-high legs. It confirms swing points, partitions each leg's range into ATR(200)‑adaptive price bins, distributes tick volume, and marks the Point of Control. The indicator draws a ZigZag and renders the profile on chart rectangles, helping you study volume concentration within each swing relative to price structure.

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.

With the multifractal parameters from Part 2 in hand, this article builds the full MMAR process. We construct the multiplicative cascade for trading time, generate Fractional Brownian Motion via Davies-Harte FFT, and combine both into X(t) = B_H[theta(t)]. A 1000-path Monte Carlo simulation produces the volatility forecast, which we then pit against GARCH on the same EURUSD M5 data. Does Mandelbrot's fractal architecture outforecast Engle's conditional variance framework? Part 3 of a eight-part series leading to a native MQL5 library and Expert Advisor.

CTrailingSlidingMedianBiLSTM is a custom MQL5 Wizard trailing module that combines robust median/MAD outlier filtering with a BiLSTM context score in the range [-1, 1]. Four algorithm modes (standard, bands, RSI, adaptive) target noise, mean-reverting bursts and liquidity spikes, reducing premature stop adjustments. This module is intended for side-by-side evaluation with diverse entry signals and money management settings.

An MQL5 script reconstructs closed trades from raw deal history and replays them on the chart bar by bar, drawing entry, exit, stop, target, and an annotation with per‑trade statistics. Four classes separate concerns: a trade data record, history reconstruction with a two‑pass SL/TP lookup and partial‑close aggregation, chart rendering, and a controller with polling‑based keyboard navigation. This enables consistent, fast visual review of each trade in its original candlestick context.

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.

We add eight shape tools and nine annotation tools to the canvas and implement a full in-place label-editing system. The article walks through geometry, AA rendering, shared word-wrap and supersampled text helpers, and the caret-driven state machine for typing, navigation, and selection. This yields a complete, consistent annotation toolkit with editable labels that plugs into the prior interaction pipeline.

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.

Manually drawn analytical object tools like Fibonacci tools, and Andrews Pitchforks are invisible to automated trading logic. This article extends a base detector to extract anchor points, level arrays, and geometric offsets from complex objects. You will implement a reusable collector that normalizes the raw chart data into structured memory arrays, ready for strategy decisions.

Part 8 adds bar-by-bar micro-trend scoring for NQ M1. GetMicroTrendStrength() builds a continuous [-1, +1] composite from EMA alignment, ATR‑normalized price position, slope consistency, and volume, with a contradiction penalty to suppress alignment/price conflicts. Session-adaptive thresholds scale by Part 7 confidence to modulate signal frequency across regimes. Outputs include a seven-state label, a binary signal, and a persistence check, calibrated on 514 New York sessions (May 2024–May 2026).

We convert the Part 15 decision‑forest classifier into a regime‑adaptive Expert Advisor that decouples statistical inference from trading authority. The EA trains on completed bars, scores each new completed bar, and confirms stable bullish, neutral, or bearish regimes before acting. It then applies spread, ownership, risk, and execution checks to authorize opening, holding, closing, or blocking a position.

In previous articles, we mentioned that sometimes we need to set a value for the ZOrder property. But why? The reason is that many pieces of code that add objects to a chart simply do not use, or more precisely do not define, a value for this property. The point is that I am not here to say what every programmer should or should not do, or how they should or should not write their code. I am here to show you, dear reader, and everyone who truly wants to understand how these processes work internally, what actually happens behind the scenes.

The article discusses the ECO optimization algorithm, which is based on ecological concepts: populations are grouped into habitats based on territorial proximity, exchange genetic material within habitats, and migrate between them. Despite its wide range of operators and elegant biological metaphor, the algorithm produced a certain result discussed below.

This article presents 'CSignalUKFCapsNet', as a custom class coded in MQL5. This class is meant to be used with the MQL5 Wizard when assembling an Expert Advisor and when selected in the Wizard it defines the Expert Advisor's entry signals. In building this custom class, we brought together the algorithm Unscented Kalman Filter and the Capsule Neural Network. Our algorithm is showcased with four operation modes, and the coding of this as a custom class for the MQL5 Wizard, allows testing with various Trailing Stop methods and Money Management systems.

This article turns the verified TDA pipeline into a live MQL5 indicator. It reduces each price window to two persistence-entropy lines (H0 and H1), computes a normalized loop-strength metric with an adaptive percentile band, and places fade marks only when loop strength is high and price hits a window extreme. You can attach the indicator, read six buffers from an Expert Advisor, and tune key window, ranking, and performance parameters.