Articles on data analysis and statistics in MQL5

In this discussion, we contrast the classical approach to time series cross-validation with modern alternatives that challenge its core assumptions. We expose key blind spots in the traditional method—especially its failure to account for evolving market conditions. To address these gaps, we introduce Effective Memory Cross-Validation (EMCV), a domain-aware approach that questions the long-held belief that more historical data always improves performance.

In this article, we will start creating the C_Orders class to be able to send orders to the trading server. We'll do this little by little, as our goal is to explain in detail how this will happen through the messaging system.

Fibonacci tools are among the most popular instruments used by technical analysts. In this article, we’ll build an Interactive Fibonacci EA that draws retracement and extension levels that react dynamically to price movement, delivering real‑time alerts, stylish lines, and a scrolling news‑style headline. Another key advantage of this EA is flexibility; you can manually type the high (A) and low (B) swing values directly on the chart, giving you exact control over the market range you want to analyze.

The article introduces the dialectical algorithm (DA), a new global optimization method inspired by the philosophical concept of dialectics. The algorithm exploits a unique division of the population into speculative and practical thinkers. Testing shows impressive performance of up to 98% on low-dimensional problems and overall efficiency of 57.95%. The article explains these metrics and presents a detailed description of the algorithm and the results of experiments on different types of functions.

For many traders, it's a familiar pain point: watching a trade come within a whisker of your profit target, only to reverse and hit your stop-loss. Or worse, seeing a trailing stop close you out at breakeven before the market surges toward your original target. This article focuses on using multiple entries at different Reward-to-Risk Ratios to systematically secure gains and reduce overall risk exposure.

We will build a biologically correct system of neurons for time series forecasting. The introduction of a plasma-like environment into the neural network architecture creates a kind of "collective intelligence," where each neuron influences the system's operation not only through direct connections, but also through long-range electromagnetic interactions. Let's see how the neural brain modeling system will perform in the market.

In this article, we explore a powerful MQL5 tool that let's you test any price level you desire with just one click. Simply enter your chosen level and press analyze, the EA instantly scans historical data, highlights every touch and breakout on the chart, and displays statistics in a clean, organized dashboard. You'll see exactly how often price respected or broke through your level, and whether it behaved more like support or resistance. Continue reading to explore the detailed procedure.

In this article, we will forecast future extreme volatility using binary classification. Besides, we will develop an extreme volatility forecast indicator using machine learning.

This is the first part of an article series presenting the implementation of bivariate copulae in MQL5. This article presents code implementing Gaussian and Student's t-copulae. It also delves into the fundamentals of statistical copulae and related topics. The code is based on the Arbitragelab Python package by Hudson and Thames.

In this discussion, we introduce a Higher-to-Lower Timeframe Synchronizer tool designed to solve the problem of analyzing market patterns that span across higher timeframe periods. The built-in period markers in MetaTrader 5 are often limited, rigid, and not easily customizable for non-standard timeframes. Our solution leverages the MQL5 language to develop an indicator that provides a dynamic and visual way to align higher timeframe structures within lower timeframe charts. This tool can be highly valuable for detailed market analysis. To learn more about its features and implementation, I invite you to join the discussion.

Often we have to take a step back and then move forward. In this article, we will show all the changes necessary to ensure that the Mouse and Chart Trade indicators do not break. As a bonus, we'll also cover other changes that have occurred in other header files that will be widely used in the future.

This article introduces a VWMA crossover signal tool for MetaTrader 5, designed to help traders identify potential bullish and bearish reversals by combining price action with trading volume. The EA generates clear buy and sell signals directly on the chart, features an informative panel, and allows for full user customization, making it a practical addition to your trading strategy.

This is my own algorithm. The article presents the Time Evolution Travel Algorithm (TETA) inspired by the concept of parallel universes and time streams. The basic idea of the algorithm is that, although time travel in the conventional sense is impossible, we can choose a sequence of events that lead to different realities.

Many traders have experienced this situation, often stick to their entry criteria but struggle with trade management. Even with the right setups, emotional decision-making—such as panic exits before trades reach their take-profit or stop-loss levels—can lead to a declining equity curve. How can traders overcome this issue and improve their results? This article will address these questions by examining random win-rates and demonstrating, through Monte Carlo simulation, how traders can refine their strategies by taking profits at reasonable levels before the original target is reached.

In this article, I introduce an innovative trading algorithm that combines evolutionary algorithms with deep reinforcement learning for Forex trading. The algorithm uses the mechanism of extinction of inefficient individuals to optimize the trading strategy.

In this article, we explore a data-driven approach to discovering and validating non-standard Fibonacci retracement levels that markets may respect. We present a complete workflow tailored for implementation in MQL5, beginning with data collection and bar or swing detection, and extending through clustering, statistical hypothesis testing, backtesting, and integration into an MetaTrader 5 Fibonacci tool. The goal is to create a reproducible pipeline that transforms anecdotal observations into statistically defensible trading signals.

Unlike what was done in the previous article, here we will test the selection option using an Expert Advisor. Although this is not a final solution yet, it will be enough for now. With the help of this article, you will be able to understand how to implement one of the possible solutions.

We have built a robust feature engineering pipeline using proper tick-based bars to eliminate data leakage and solved the critical problem of labeling with meta-labeled triple-barrier signals. This installment covers the advanced labeling technique, trend-scanning, for adaptive horizons. After covering the theory, an example shows how trend-scanning labels can be used with meta-labeling to improve on the classic moving average crossover strategy.

Enhance your market analysis with the MQL5-native Candlestick Probability EA, a lightweight tool that transforms raw price bars into real-time, instrument-specific probability insights. It classifies Pinbars, Engulfing, and Doji patterns at bar close, uses ATR-aware filtering, and optional breakout confirmation. The EA calculates raw and volume-weighted follow-through percentages, helping you understand each pattern's typical outcome on specific symbols and timeframes. On-chart markers, a compact dashboard, and interactive toggles allow easy validation and focus. Export detailed CSV logs for offline testing. Use it to develop probability profiles, optimize strategies, and turn pattern recognition into a measurable edge.

We will look at price discretization methods using Python + MQL5. In this article, I will share my practical experience developing a Python library that implements a wide range of approaches to bar formation — from classic Volume and Range bars to more exotic methods like Renko and Kagi. We will consider three-line breakout candles and range bars analyzing their statistics and trying to define how else the prices can be represented discretely.

The article considers a new population optimization algorithm - Cyclic Parthenogenesis Algorithm (CPA), inspired by the unique reproductive strategy of aphids. The algorithm combines two reproduction mechanisms — parthenogenesis and sexual reproduction — and also utilizes the colonial structure of the population with the possibility of migration between colonies. The key features of the algorithm are adaptive switching between different reproductive strategies and a system of information exchange between colonies through the flight mechanism.

This article proposes an asset screening process for a statistical arbitrage trading strategy through cointegrated stocks. The system starts with the regular filtering by economic factors, like asset sector and industry, and finishes with a list of criteria for a scoring system. For each statistical test used in the screening, a respective Python class was developed: Pearson correlation, Engle-Granger cointegration, Johansen cointegration, and ADF/KPSS stationarity. These Python classes are provided along with a personal note from the author about the use of AI assistants for software development.

This article explains how to design and optimise a trading system using the Detrended Price Oscillator (DPO) in MQL5. It outlines the indicator's core logic, demonstrating how it identifies short-term cycles by filtering out long-term trends. Through a series of step-by-step examples and simple strategies, readers will learn how to code it, define entry and exit signals, and conduct backtesting. Finally, the article presents practical optimization methods to enhance performance and adapt the system to changing market conditions.

The article describes the experience of developing a hybrid trading system that combines classical technical analysis with neural networks. The author provides a detailed analysis of the system architecture from basic pattern analysis and neural network structure to the mechanisms behind trading decisions, and shares real code and practical observations.

This article presents a study of the interaction of different activation functions with optimization algorithms in the context of neural network training. Particular attention is paid to the comparison of the classical ADAM and its population version when working with a wide range of activation functions, including the oscillating ACON and Snake functions. Using a minimalistic MLP (1-1-1) architecture and a single training example, the influence of activation functions on the optimization is isolated from other factors. The article proposes an approach to manage network weights through the boundaries of activation functions and a weight reflection mechanism, which allows avoiding problems with saturation and stagnation in training.

This article explores the unique identity of each currency pair through the lens of its historical price action. Inspired by the concept of genetic DNA, which encodes the distinct blueprint of every living being, we apply a similar framework to the markets, treating price action as the “DNA” of each pair. By breaking down structural behaviors such as volatility, swings, retracements, spikes, and session characteristics, the tool reveals the underlying profile that distinguishes one pair from another. This approach provides more profound insight into market behavior and equips traders with a structured way to align strategies with the natural tendencies of each instrument.

The article describes an innovative approach to forecasting price movements in financial markets using quantum computing. The main focus is on the application of the Quantum Phase Estimation (QPE) algorithm to find prototypes of price patterns allowing traders to significantly speed up the market data analysis.

In the previous article, we introduced the multi-agent adaptive framework MASAAT, which uses an ensemble of agents to perform cross-analysis of multimodal time series at different data scales. Today we will continue implementing the approaches of this framework in MQL5 and bring this work to a logical conclusion.

This is an article that I have written aimed to expound and explain Fair Value Gaps, their formation logic for occurring, and automated trading with breakers and market structure shifts.

Dynamic mode decomposition (DMD) is a technique usually applied to high-dimensional datasets. In this article, we demonstrate the application of DMD on univariate time series, showing its ability to characterize a series as well as make forecasts. In doing so, we will investigate MQL5's built-in implementation of dynamic mode decomposition, paying particular attention to the new matrix method, DynamicModeDecomposition().

This article describes a simple but comprehensive statistical arbitrage pipeline for trading a basket of cointegrated stocks. It includes a fully functional Python script for data download and storage; correlation, cointegration, and stationarity tests, along with a sample Metatrader 5 Service implementation for database updating, and the respective Expert Advisor. Some design choices are documented here for reference and for helping in the experiment replication.

This article presents Fractal Reaction System, a compact MQL5 system that converts fractal pivots into actionable market-structure signals. Using closed-bar logic to avoid repainting, the EA detects Change-of-Character (ChoCH) warnings and confirms Breaks-of-Structure (BOS), draws persistent chart objects, and logs/alerts every confirmed event (desktop, mobile and sound). Read on for the algorithm design, implementation notes, testing results and the full EA code so you can compile, test and deploy the detector yourself.

Today we will begin the second stage, where we will look at the market replay/simulation system. First, we will show a possible solution for cross orders. I will show you the solution, but it is not final yet. It will be a possible solution to a problem that we will need to solve in the near future.

The article presents the Big Bang - Big Crunch method, which has two key phases: cyclic generation of random points and their compression to the optimal solution. This approach combines exploration and refinement, allowing us to gradually find better solutions and open up new optimization opportunities.

In Part 38, we build a production-grade MT5 monitoring panel that converts raw ticks into actionable signals. The EA buffers tick data to compute tick-level VWAP, a short-window imbalance (flow) metric, and ATR-based position sizing. It then visualizes spread, ATR, and flow with low-flicker bars. The system calculates a suggested lot size and a 1R stop, and issues configurable alerts for tight spreads, strong flow, and edge conditions. Auto-trading is intentionally disabled; the focus remains on robust signal generation and a clean user experience.

The Black Hole Algorithm (BHA) uses the principles of black hole gravity to optimize solutions. In this article, we will look at how BHA attracts the best solutions while avoiding local extremes, and why this algorithm has become a powerful tool for solving complex problems. Learn how simple ideas can lead to impressive results in the world of optimization.