Articles on data analysis and statistics in MQL5

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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.

Read about the fuzzy logic, digital filters, market profile, Kohonen maps, neural gas and many other tools that can be used for trading.

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Foundation Models for Trading (Part III): Running a Generative AI Forecaster Inside MetaTrader 5

Foundation Models for Trading (Part III): Running a Generative AI Forecaster Inside MetaTrader 5

We demonstrate live forecast charting with Kronos in MQL5 and an evaluation pipeline designed to be look‑ahead‑safe. Deterministic dumps are scored per horizon against a random‑walk baseline (15,113 predictions), then fed to a simple Strategy Tester rule on EURUSD H1. The findings show no edge, and illustrate how a high threshold can yield a persuasive but low‑information backtest with very few trades.
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Automated Trade Statement Exporter to Excel-Compatible XLSX in MQL5

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.
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Building AI-Powered Trading Systems in MQL5 (Part 11): Optimizing the UI with Frame Throttling and Partial Rendering

Building AI-Powered Trading Systems in MQL5 (Part 11): Optimizing the UI with Frame Throttling and Partial Rendering

We optimize an MQL5 canvas interface to stay responsive under rapid input without changing its appearance. The article adds a direct-buffer canvas for block region copies, caches text widths and glyph coverage, caps repaints at 60 fps (16 ms), and limits drawing to panes and regions that actually changed. As a result, hover, scroll, and popups render smoothly without full-panel redraws.
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Implementing an LLM Agent with SQL Memory in MetaTrader 5

Implementing an LLM Agent with SQL Memory in MetaTrader 5

An LLM agent with SQL memory in MetaTrader 5 — an architecture that eliminates the main limitation of traditional LLM Expert Advisors (EAs): the loss of context between queries. Each agent decision is recorded in SQLite along with the market conditions at the time of the signal — RSI, MA alignment, volatility — and after the position is closed, the outcome is written to the database. When the next request comes in, the agent reviews its own history — similar past RSI conditions and the last three agent decisions — and only then analyzes the current market. The result is a system that remembers its errors between restarts and adapts its behavior based on accumulated statistics, rather than starting from scratch with each new bar.
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Isolation Forest: Unsupervised Anomaly Detection, and What It Actually Finds in Price Data

Isolation Forest: Unsupervised Anomaly Detection, and What It Actually Finds in Price Data

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.
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Working with ONNX Models in MQL5 (Part 1): Decoding the Model File with a Protobuf Parser

Working with ONNX Models in MQL5 (Part 1): Decoding the Model File with a Protobuf Parser

We decode ONNX files in pure MQL5 by implementing a Protocol Buffers reader from scratch. We generate a sample network in Python, verify it in Netron, and then parse the same binary to recover graph nodes, connections, weight tensors, and input/output shapes. The result is a MetaTrader 5 program that inspects a trained model's structure before inference, without any external libraries.
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Price Action Analysis Toolkit Development (Part 87): Searching Chart History with Recorded Double-Bottom Samples

Price Action Analysis Toolkit Development (Part 87): Searching Chart History with Recorded Double-Bottom Samples

This stage connects structural validation with reference matching for double bottoms. The Expert Advisor scans completed history, filters pairs by the current structural rules, and compares normalized close and low profiles against validated samples from the library. Results that meet the similarity requirement appear in the panel for chart review and are saved to REFERENCE_MATCHES.csv.
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The MQL5 Standard Library Explorer (Part 15): Building a Market-Regime Classifier with dataanalysis.mqh

The MQL5 Standard Library Explorer (Part 15): Building a Market-Regime Classifier with dataanalysis.mqh

This part focuses on practical data analysis in MQL5 with dataanalysis.mqh. We prepare a labeled dataset from bars, apply normalization, explore redundancy with PCA, and train a decision forest to classify future bar regimes. The article shows how to obtain out-of-bag estimates and permutation importance, helping you validate the model and understand which inputs matter most.
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Competitive Swarm Optimizer (CSO)

Competitive Swarm Optimizer (CSO)

The article discusses the Competitive Swarm Optimizer — a swarm optimization algorithm based on an extremely simple idea: agents are randomly paired, and the loser learns from the winner and is drawn toward the center of the swarm. In addition to analyzing CSO, the article describes the modernization of the test bench: visualization of the algorithms’ operation has been moved into 3D space, making it possible to clearly observe the movement of the population on the surface of the test function.
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Drawdown Duration Analysis Indicator in MQL5

Drawdown Duration Analysis Indicator in MQL5

We build a drawdown analytics dashboard that derives the equity curve from deals and finds every episode's depth and recovery duration. Results appear on a CCanvas timeline spaced by point index with alternating bold annotations, and in a terminal table sorted by duration, allowing you to prioritize risk by time spent underwater rather than depth alone.
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Ebola Optimization Search Algorithm (EOSA)

Ebola Optimization Search Algorithm (EOSA)

The article examines the EOSA algorithm, which is inspired by the mechanisms of Ebola virus transmission: short-distance transmission through close contact (exploitation) and long-distance transmission through travel (exploration). An analysis of the original publication revealed critical issues in the mathematical formulas and an epidemiological model that was impractical to implement, which required a significant overhaul of the algorithm to produce a workable implementation.
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Market Simulation: Position View (X)

Market Simulation: Position View (X)

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.
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Monte Carlo Simulation and Analysis for MetaTrader 5 Backtest Reports

Monte Carlo Simulation and Analysis for MetaTrader 5 Backtest Reports

This article explains Monte Carlo simulation and analysis for trading and guides you through a Python tool that ingests MetaTrader 5 HTML reports. It generates many randomized equity paths, then summarizes them with max drawdown, bust/profit rates, and percentile envelopes around the mean curve. The workflow helps you assess uncertainty, separate normal behavior from outliers, and size positions accordingly.
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Does Your EA Depend on Candle Boundaries? A Shifted-Bar Stress Test in MQL5

Does Your EA Depend on Candle Boundaries? A Shifted-Bar Stress Test in MQL5

The framework evaluates boundary sensitivity by rebuilding shifted target-timeframe bars from completed M1 sources and running one Strategy Tester pass for each boundary offset. It includes a ShiftedBarBuilder, a demonstration EA, and a deterministic self-test. An XAUUSD M15 case study reports net profit, Profit Factor, maximum relative equity drawdown, and total trades across all 15 offsets to quantify dependence on the bar grid.
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Building AI-Powered Trading Systems in MQL5 (Part 10): A Resolution-Independent Vector Icon System

Building AI-Powered Trading Systems in MQL5 (Part 10): A Resolution-Independent Vector Icon System

We replace the embedded bitmap icons in our MQL5 canvas interface with a resolution-independent vector icon system. A small set of anti-aliased primitives (strokes, discs, rings, rounded rectangles, and polygons) draws every logo and sidebar glyph procedurally, then plugs into the header, sidebar, and theme toggle. You get smaller builds, theme-aware recoloring, and icons that stay sharp at any size.
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The Repository Pattern in MQL5: Abstracting Trade History Access for Testable EA Logic

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.
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Adaptive Position Sizing in MQL5: A Prototype Risk Engine with Generalized Kelly and Bootstrap Calibration

Adaptive Position Sizing in MQL5: A Prototype Risk Engine with Generalized Kelly and Bootstrap Calibration

This article presents a modular position sizing engine for MetaTrader 5 that operates on normalized R-multiples. A layered pipeline combines enriched trade statistics, a generalized Kelly edge estimate, volatility-aware adjustment, Monte Carlo calibration under ruin and drawdown limits, a continuous risk policy, an exposure guard, and a broker-aware lot calculator. The output is a broker-valid lot size with an optional CSV audit trail, providing a transparent prototype for implementing modern risk controls in native MQL5.
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Working with ONNX Models in MQL5 (Part 2): Drawing the Model Graph on an Interactive Chart Panel

Working with ONNX Models in MQL5 (Part 2): Drawing the Model Graph on an Interactive Chart Panel

We turn the ONNX reader into an interactive graph viewer on a MetaTrader 5 chart. The parser is extended to carry tensor shapes and node attributes, and a canvas with anti-aliased drawing renders nodes and labeled connections. The layout arranges layers by depth, while zoom, pan, and clicks let you inspect operators and the tensors they read. This makes a model's structure and data flow visible directly in MQL5.
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Price Action Analysis Toolkit Development (Part 81): Adding Persistent Historical Bookmarks to an MQL5 Navigator

Price Action Analysis Toolkit Development (Part 81): Adding Persistent Historical Bookmarks to an MQL5 Navigator

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.
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The Deflated Sharpe Ratio in MQL5: Telling a Real Edge from a Lucky Backtest

The Deflated Sharpe Ratio in MQL5: Telling a Real Edge from a Lucky Backtest

A Sharpe ratio read off the best of many optimization runs is not the number it looks like. This article ships a reusable native CDeflatedSharpe class that turns a raw Sharpe into an honest confidence statement. The Probabilistic Sharpe Ratio corrects it for sample length and for skew and kurtosis; the Deflated Sharpe Ratio adds the correction almost nobody applies, for the number of variants you tried before keeping the best. Everything is from scratch, the sample moments, the normal CDF and its inverse included, so there is no Python, no DLL and no library. On a real sweep of 56 moving-average variants on XAUUSD the winner looked significant at 98.5 percent by PSR, then fell to 90.6 percent once the 56 trials were admitted, below the usual bar. That gap is the selection bias, made measurable.
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Evolutionary Selection of LLM Agents in MetaTrader 5

Evolutionary Selection of LLM Agents in MetaTrader 5

The article describes the architecture of a trading system consisting of 20 Grok (xAI)-based LLM agents, each of which embodies a unique trading philosophy — from pure momentum to a statistical z-score. The system applies a genetic algorithm directly during trading: every 20 trades, it automatically eliminates weak agents, clones strong ones with a prompt mutation, and publishes a leaderboard on the MetaTrader 5 chart — without interrupting trading and without using any SDK.
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Symbolic Fourier Approximation in MQL5: Benchmarking SFA Against SAX

Symbolic Fourier Approximation in MQL5: Benchmarking SFA Against SAX

We implement Symbolic Fourier Approximation in MQL5 and compare it to SAX under a shared harness on identical price windows. SFA keeps low‑frequency Fourier coefficients and learns per‑position bins (MCB), with a proven, sound lower bound. The measurements show how the same bit budget behaves under different splits of word length and alphabet, and give a practical rule for choosing settings for your symbol.
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Defining your Edge (Part 6): Harnessing Fourier Transform and a Spiking Neural Network in an Expert Advisor

Defining your Edge (Part 6): Harnessing Fourier Transform and a Spiking Neural Network in an Expert Advisor

Article revisits Trading Robot that merged Discrete Fourier Transform with Leaky Integrate-and-Fire Spiking Neural Network. Evaluation is made over the seven operating modes with different symbols, timeframes, and test windows. We use two-thirds of the test window to optimize while the one-third does a forward walk run. This study tries to detail parameter interactions, input scaling, gating effects, and outlines practical checks that include rolling windows, frozen inputs, and others. The goal remains identifying settings worth further testing or paper trading.
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Building Volatility Models in MQL5: Implementing the APARCH Volatility Process

Building Volatility Models in MQL5: Implementing the APARCH Volatility Process

The article introduces the APARCH volatility process to the MQL5 library via the CAparchProcess class, estimating the power exponent (delta) jointly with other parameters. It details the recursion, parameter bounds, stationarity constraints, and starting values and reports SLSQP solver updates that streamline optimization. Implementation correctness is partially validated by reproducing approximations of GARCH and GJR-GARCH conditional volatility under parameter restrictions. A companion APARCH indicator visualizes conditional volatility, standardized residuals, and delta to track volatility dynamics and parameter drift.
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Defining your Edge (Part 5): Using GARCH Variance and Volatility-Scaled LSTM in an Expert Advisor

Defining your Edge (Part 5): Using GARCH Variance and Volatility-Scaled LSTM in an Expert Advisor

We merge GARCH(1,1) variance projections with ATR plus Bollinger-Bands patterns to form an algorithm that could optionally be used with volatility-scaled LSTM within LSTM Wizard-ready signal class. We cover feature scaling, mode scoring, thresholds, and safety checks. Readers can replicate backtest/forward test results to verify if the recurrent layer gives incremental discrimination over our deterministic baseline.
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Building a Session Performance Analytics Dashboard in MQL5

Building a Session Performance Analytics Dashboard in MQL5

This article builds an MQL5 dashboard that classifies closed deals into Sydney, Tokyo, London, and New York trading sessions by UTC close time. It computes per-session P&L, win rate, and average hold time, then renders the results as a persistent CCanvas bar chart with an account-wide summary row, alongside an Experts tab summary table. A verification script confirms the classification and metrics logic behaves correctly.
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Price Action Analysis Toolkit Development (Part 84): Validating Recorded Double-Bottom Samples

Price Action Analysis Toolkit Development (Part 84): Validating Recorded Double-Bottom Samples

This work adds an explainable validation module to the recording toolkit for double bottoms. It finds and filters swing lows, selects the neckline, quantifies depth, low similarity, symmetry and recovery, and assigns a rule-based status and scores accepted pairs. The settings are configurable, the process is reproducible, and the original sample data remains intact for comparison across rule sets.
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Generating a Per-Symbol Trade Analytics PDF Report from MQL5

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.
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Using Renko-bar Regression with Error Correction

Using Renko-bar Regression with Error Correction

The article presents a regression-based approach to forecasting Renko bars using CatBoost: the model estimates the logarithmic return of the next bar and the uncertainty of the forecast. We will examine a cascade of residual models with OOF validation using TimeSeriesSplit, shrinkage, and overall early stopping, as well as conditional bias correction. On EURUSD D1, a reduction in OOF-MAE was achieved, along with approximately 65% directional accuracy. A working script for MetaTrader 5 is provided that generates a signal, position size, SL, and TP in brick units.
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MetaTrader 5 Machine Learning Blueprint (Part 21): Feature Importance Analysis

MetaTrader 5 Machine Learning Blueprint (Part 21): Feature Importance Analysis

Feature importance often understates correlated predictors by spreading one signal across many engineered copies, while unrelated noise can appear higher. We measure this effect against a known ground truth and compare four remedies: permutation importance with purged cross-validation, single-feature models, and clustered impurity versus clustered accuracy. The results include per-method rankings and a per-cluster dilution ratio that help identify true signals and avoid deleting valuable features.
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Position Management: Deriving a Self-Calibrating Exit Ladder From Historical MFE in MQL5

Position Management: Deriving a Self-Calibrating Exit Ladder From Historical MFE in MQL5

We implement three MQL5 classes that replace fixed 1R/2R/3R targets with data-driven scale-out levels. CExcursionTracker records each closed trade's maximum favorable excursion in R, CExitLadderCalibrator derives runs from distribution percentiles with lookback and minimum-sample controls, and CLadderExecutor executes them on open positions. The ladder recalibrates as trades accumulate and uses a fallback until enough samples exist.
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Practical Modules from Other Languages in MQL5 (Part 08): MATPLOTLIB

Practical Modules from Other Languages in MQL5 (Part 08): MATPLOTLIB

Learn how to bring advanced plotting and data visualization to the MetaTrader 5 terminal by leveraging Matplotlib, one of Python's most powerful and widely used visualization libraries.
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Market Simulation: Position View (XV)

Market Simulation: Position View (XV)

In this article, I will try to explain as simply as possible how messaging between applications can be used. The goal is to enable you to create something workable in the simplest and most efficient way possible whenever you can. I am not sure if I will be able to convey the idea behind this concept, since it is not that easy to understand for someone encountering it for the first time. In addition, I will take this opportunity to show you how to modify the replay/simulation system so you can debug an Expert Advisor or any other code you are developing. And all of this is just as simple and straightforward.
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Creating and Testing a Council of 15 Models in MetaTrader 5

Creating and Testing a Council of 15 Models in MetaTrader 5

The article describes the transition from four-voice debates to the Council of Fifteen: ten analysts, four independent risk managers, and a Chair, with strict voting rules. It examines the roles of the participants, the three-phase architecture, and the parallel execution of a full cycle in 10–15 seconds. It shows the operational log, the risk-gate rules, and backward compatibility so you can quickly connect the system to an Expert Advisor.
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Encoding Candlestick Patterns (Part 5): Expanding Taxonomy of Candlestick for General Pattern Frequency Analysis

Encoding Candlestick Patterns (Part 5): Expanding Taxonomy of Candlestick for General Pattern Frequency Analysis

This article extends the candlestick encoding framework by separating previously unclassified bullish and bearish candlesticks into distinct symbols. Using an MQL5 script, historical data were automatically encoded, sequential patterns were extracted, and frequency statistics were generated. The results show that these newly identified candles represent a significant portion of market activity, revealing structural information previously hidden by the generic underscore notation. The expanded taxonomy improves the completeness of the symbolic representation while preserving an objective, quantitative framework for large-scale market structure analysis.
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Market Simulation: Position View (XIV)

Market Simulation: Position View (XIV)

Now we will implement this solution, since MQL5 is based on the same principles as event-driven programmingю Developers often use this model when creating DLLs. I know that at first, the event-driven model will seem confusing and illogical. But in this article, I will explain the principles of event-driven programming in a way that is easier to understand, so that if you are just getting started, you will have a clear grasp of how it works. Understanding what I am about to explain in this article will help you throughout your work as a programmer.
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Trade Duration vs Profitability Scatter Plot Indicator in MQL5

Trade Duration vs Profitability Scatter Plot Indicator in MQL5

The article presents a compact dashboard that relates trade duration to net profit using MQL5 and CCanvas. It pulls closed deals, derives duration in minutes, and renders a log‑scaled scatter by symbol, with an overlaid least‑squares line and R². A bucketed duration view identifies which hold‑time range produced the highest average result, helping assess exit timing.
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Replay and Market Simulation: The Grand Finale

Replay and Market Simulation: The Grand Finale

I know that many of you may have thought I would publish a few more articles to explain other aspects of this system. The missing elements are easy to implement. Even so, developing them will let you see how prepared you really are.
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Defining your Edge (Part 4): Applying Isotonic Regression and PNN Price-Forecasting in an Expert Advisor

Defining your Edge (Part 4): Applying Isotonic Regression and PNN Price-Forecasting in an Expert Advisor

We consider the methods with which Isotonic Regression calibrates raw RSI, Stochastic and price-action signal scores into probabilities that are sorted, while a separate Probability based Neural Network evaluates similar historical market states. This article uses both approaches in a ready-made MQL5 custom signal class that is compatible with MQL5 Wizard and provides up to 7 selectable entry modes. Reproducible tests compare isotonic-only signals with the combined Isotonic-PNN model to assess whether the network adds useful information beyond the simpler baseline.
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Market Simulation: Position View (VI)

Market Simulation: Position View (VI)

In this article, we will implement a number of improvements to ensure that the position indicator accurately reflects the actual state on the trading server in terms of open positions and their current state. I should point out that the applications shown here are in no way intended to replace any of the elements available in MetaTrader 5. They should also not be used without due caution and a balanced approach, since their purpose is to provide educational code—that is, code intended solely for learning how the system works. The reason I call this code “educational” is that, in some cases, using messages is not the best way to implement certain functions.