Articles on data analysis and statistics in MQL5
Articles on mathematical models and laws of probability are interesting for many traders. Mathematics is the basis of technical indicators, and statistics is required to analyze trading results and develop strategies.
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Dendritic Cell Algorithm (DCA)
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.
Persistent Homology in MQL5: The Reduction Algorithm and the Persistence Diagram
We complete persistent homology for MQL5 by reducing the Vietoris–Rips boundary matrix to a persistence diagram. The article implements Z/2 column reduction (CTDAReduction), a diagram container with analytics (CTDADiagram), and a facade that runs the six-stage pipeline in one call (CTDA). Outputs are cross-checked against Ripser to numerical agreement, enabling reliable diagram-based metrics.
CSV Data Analysis (Part 1): CSV Export Engine for MQL5 Multi-Core Optimizations
Multi-core optimization in MetaTrader 5 can silently drop results when parallel agents contend for the same CSV file. A reusable MQL5 export engine applies an iteration-based spin-lock to acquire the file handle reliably and append rows without loss. It persists custom metrics such as the Sortino Ratio, average trade duration, and signal-quality measures (lag and whipsaws) into a consolidated CSV for downstream analysis.
MQL5 Wizard Techniques you should know (Part 96): Using Wavelet Thresholding and LSTM Network in a Custom Money Management Class
In this article we consider a custom MQL5 Wizard class that processes Money Management. Our custom class is labelled ‘CMoneyWaveletLSTM’, and is developed by combining the Wavelet Thresholding algorithm with an LSTM network. As has been the case throughout these series, the developed model is testable with MQL5 Wizard-Assembled Expert Advisors that can be tuned with different trailing stops and entry Signals classes. We maintain our entry Signal, as in past articles as the built-in 'Envelopes' class and the RSI class.
From Option Chain to 3D Volatility Surface in MetaTrader 5
This article walks through creating an MT5 indicator that ingests option chains from native symbols or CSV, inverts prices to implied volatility via a hybrid Newton–Raphson/bisection method, and assembles a clean strike–expiry grid. It then renders a shaded, rotatable 3D surface with the platform's DirectX layer, enabling clear, in-terminal analysis of skew and term structure using live or file-based data.
Learnable Curves, Not Weights: A Kolmogorov-Arnold Network from Scratch
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.
Persistent Key-Value Store in MQL5: Using Flat Files as a Lightweight Database for EA State
A lightweight persistence design lets EAs retain counters, flags, and timestamps between terminal restarts. Using only MQL5, CPersistentStore writes a human-readable key=value file in MQL5/Files and serves reads from a CHashMap write-through cache via a typed API. The article analyzes O(1)/O(n) operations, partial‑write risks, and lack of locking, compares with GlobalVariables/SQLite, and provides a demo that reloads state deterministically.
Exponentially Weighted Covariance Matrix in MQL5: Building an Adaptive Correlation Monitor for Multi-Symbol EAs
This article builds a constant-memory EW covariance engine and a chart heatmap for monitoring cross-symbol correlations in MQL5. CEWCovariance updates in O(N²) time per bar and exposes covariance/correlation accessors; CHeatmapRenderer shows a five‑symbol matrix with values and colors. You will learn λ-to‑window mapping, how to set a meaningful min_obs warm‑up, and how to size the variance guard epsilon for real FX M1 data.
Building a Compile-Time Unit Testing Framework in MQL5 Using Preprocessor Assertions
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.
Market Simulation: Position View (IX)
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.
Market Simulation: Getting started with SQL in MQL5 (I)
In today's article we will begin studying the use of SQL in MQL5 code. We will also look at how to create a database. Or, more precisely, how to create a SQLite database file using the features built into MQL5. We will also see how to create a table, and then how to establish a relationship between tables by using primary and foreign keys. All of this, once again, will be done with MQL5. We will see how easy it is to create code that can later be migrated to other SQL implementations by using a class that helps hide the implementation being created. And, most importantly, we will see that at various points we may face the risk that something will go wrong when using SQL. This happens because, in MQL5 code, SQL code will always be placed inside a string.
Beyond GARCH (Part V): Fitting the Multifractal Spectrum in MQL5
This article builds the Spectrum Fitter: from tau(q) we compute f(alpha) with a discrete Legendre transform, then fit Normal, Binomial, Poisson, and Gamma spectra under box constraints using BLEIC. The best model by SSE is selected, and its parameters (eg, alpha min, alpha max or alpha_0, gamma) become the cascade inputs for multifractal simulation.
MQL5 Wizard Techniques you should know (Part 99): Using a KD-Tree and an Echo State Network in a Custom Money Management Class
This article lays out 'CMoneyKDTreeESN' custom money management class usable with the MQL5 Wizard, that combines the KD-Tree algorithm and the Echo State Network. We use the KD-Tree on log returns and ATR to give us a risk score, while the ESN tracks recent flow to give us a bounded lot size multiplier. Our class is usable in a variety of Wizard assembled Expert Advisors as shown here with the Envelopes and RSI signals, with a broad objective of modulating exposure in high-volatility and tail-risk environments.
Dandelion Optimizer (DO)
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.
Beyond GARCH (Part VI): Fractional Brownian Motion And The Multiplicative Cascade in MQL5
This article implements the MMAR Simulation Engine that turns fitted parameters (H, distribution, coefficients, sample volatility) into synthetic price paths. It builds multifractal trading time via a multiplicative cascade, synthesizes fractional Brownian motion with Davies–Harte or Cholesky, scales it to target volatility, and composes the process by time deformation. Readers get a reusable MQL5 class, method choices by path length, and validation steps for scenario testing and Monte Carlo use in the next part.
Enhancing the MQL5 Portfolio Analyzer Dashboard: Active Mitigation, Data Exports, and AI Integration
This article delivers active drawdown monitoring, automated mitigation rules, Excel XML data export, and AI-assisted review for the Portfolio Analyzer dashboard. It visualizes strategy-level drawdowns over time, enforces limits by closing positions and optionally disabling AutoTrading, and generates structured spreadsheets from trade records. A hybrid MQL5-Python approach runs the external review script directly from the terminal, supporting practical risk control and transparent reporting.
Market Simulation: Position View (XII)
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.
Network Momentum for MetaTrader5: Trading the Lead-Lag Graph Between Markets
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.
CSV Data Analysis (Part 6): Multi-Broker Result Normalization and Cross-Platform CSV Reconciliation
This article presents a multi‑broker CSV normalization framework. An MQL5 include file enriches exports with broker metadata. A Python module resolves schema divergences — pip conventions, symbol aliases, time offsets, commission models, and currency denomination — producing a unified canonical dataset. Comparative visualizations of slippage distributions and net‑of‑cost performance enable reliable cross‑platform strategy analysis without silent data corruption.
Real-Time Trade Event Logger to SQLite via MQL5 DLL Bridge
The article shows how to build an MQL5 EA that writes every deal to an SQLite database the moment it appears, using the built-in Database API as the SQLite bridge. It implements an event data model, a prepared INSERT workflow reused across calls, session-safe recovery after restarts, and deal detection via OnTrade(). You can open the resulting file with any SQLite client to run queries for analysis and reporting.
MQL5 Wizard Techniques you should know (Part 94): Using Reservoir Sampling and Linear Regression in a Custom Trailing Stop Class
For this article we rotate to a custom MQL5 Wizard class implementation that explores Trailing Stops. Our custom class is ‘CTrailingReservoirLinReg’ that we derive by combining the Reservoir Sampling algorithm with a Linear Regression network. As has been the case throughout these series, this formulation is testable with MQL5 Wizard Assembled Expert Advisors that can be tuned with various entry signals and money management classes.
Rolling Sharpe Ratio with Statistical Significance Bands in MQL5
This article presents a custom MetaTrader 5 indicator that computes a rolling annualized Sharpe ratio and plots configurable z-score significance bands based on Lo's asymptotic standard error. It uses a circular return buffer with incremental variance to keep O(1) updates. We explain the n^(-1/2) uncertainty scaling, the inflation of intervals at high Sharpe values, and how to set per-instrument annualization for correct deployment.
Market Simulation: Position View (IV)
Here we will start bringing together different components or applications that were previously completely isolated from each other. Chart Trade, the mouse indicator, and the Expert Advisor had already been linked to one another, but there was still no way to directly display on the chart the positions open on the trading server, which are often managed using a cross-order system. From this point on, this becomes possible, opening the way for various ideas and future implementations. Although we are only beginning to put these components into operation, we already have a direction for further development.
Beyond GARCH (Part VII): Monte Carlo Volatility Forecasting in MQL5
We implement the CMonteCarlo module that turns the fitted MMAR parameters into a volatility forecast via Monte Carlo. It runs N independent simulations over a chosen horizon and reports mean, median, standard deviation, and a percentile-based 95% confidence interval, with access to per-run values if needed. Adaptive cascade depth selects the minimal k such that b^k covers the horizon, keeping the run fast and consistent.
Building a Gold Volatility Regime Monitor from Options Data in MQL5
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.
Market Simulation: Position View (VIII)
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.
Implementing and Benchmarking Bag-of-SFA-Symbols (BOSS) Against Dynamic Time Warping (DTW)
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.
Market Simulation: Position View (VII)
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.
Ecological Cycle Optimizer (ECO)
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.
Deterministic Dendritic Cell Algorithm (dDCA)
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.
Building Volatility Models in MQL5 (Part V): Implementing EGARCH as an Alternate Asymmetric Volatility Process
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.
Automated Trade Statement Exporter to Excel-Compatible XLSX in MQL5
An MQL5 script reconstructs closed trades from deal history using a two-pass SL/TP lookup and exports them to an Excel-compatible XLSX file without third-party libraries. Four cooperating classes handle trade data, history reconstruction, SpreadsheetML XML generation, and ZIP assembly via .NET's ZipFile class through a direct ShellExecuteW call with marker-file polling. The output opens in Excel and Google Sheets with correct numeric types, formatted date columns, and a bold header row.
Motifs and Discords: Building a Matrix Profile from Scratch
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.
The Repository Pattern in MQL5: Abstracting Trade History Access for Testable EA Logic
Direct calls to the MQL5 History API inside analytics components create hidden terminal dependencies that make isolated testing structurally impossible. This article constructs an ITradeRepository abstraction layer with CLiveTradeRepository and CMockTradeRepository implementations, enabling the same analytics engine and equity curve panel to operate identically against live account data or a deterministic in-memory dataset. Repository injection eliminates direct API coupling, supports offline validation, and confines data source changes to a single implementation class.
Market Simulation: Position View (XIII)
In this article, we will look at how to easily implement an indicator that shows whether a position is generating a profit or a loss. The procedure is simple and effective. Even without in-depth expertise, this indicator will allow you to easily recognize when to close a position. This way, you will avoid unexpected results, since the calculation reflects the actual outcome you would get if you closed the position.
Exporting Symbol Tick Data to Binary Files in MQL5 for Offline Analysis
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.
Combining 3D Bars, Quantum Computing, and Machine Learning into a Unified Trading System
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.
Foundation Models for Trading (Part II): Decoding, Autoregression, and an Exact KV-Cache
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.
Survival Analysis for Trade Exits: A Discrete-Time Competing-Risks Model in MQL5
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.
Generating a Per-Symbol Trade Analytics PDF Report from MQL5
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.