Articles on data analysis and statistics in MQL5
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Implementing and Comparing Five Historical Volatility Estimators in MQL5
The study implements five historical-variance estimators in MQL5 and evaluates their one-session-ahead persistence forecasts for EURUSD D1 sessions using an M1 realized-variance proxy. Deterministic tests cover formulas, chronological order, and target construction. A configurable indicator, comparison scripts, and CSV outputs provide reproducible losses, calibration diagnostics, a common‑target mask, and sensitivity to the estimation window.
Win Rate and Edge Ratio Heatmap by Hour and Symbol in MQL5
This MQL5 dashboard aggregates closed deals by symbol and UTC hour, calculates win rate and average reward‑to‑risk, and displays the results as two color‑coded heatmaps. A companion table in the Experts tab highlights the strongest and weakest symbol/hour cells, with an option to require a minimum trade count to reduce noise.
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.
Swarm Optimizer with Hierarchical Sub-Flocks — Flock by Leader
We are developing and implementing the Flock by Leader algorithm in MQL5: sub-flocks are formed based on the ARF metric, and the leader is determined by the highest personal best rather than by the centroid's position. We present the update formulas for the swarm roles and the separation mechanism. The C_AO_FBL class is compatible with the test bench and has been tested on the Hilly, Forest, and Megacity functions with dimensionalities from 10 to 1000 coordinates, which simplifies reproduction and comparison.
Market Replay: Unity Is Strength (I)
We're entering the home stretch. The development of the replay/simulation system is nearly complete. Of course, we still have a few things left to finish, but compared to everything we've already done, completing what's left won't be difficult. However, it is essential to fully absorb and understand everything covered in this article. So I hope you enjoy reading this and, above all, that you enjoy this final stage of the journey.
Did Your Scale Outs Actually Help? A Scale Out Value Analyzer in MQL5
The article presents an MQL5 tool that tests whether scaling out improved results rather than only appearing disciplined. It reconstructs positions from closing-deal history and reprices the full volume at the first, last, and best exit rates actually achieved, producing a Value-Add Ratio, a Scale-Out Win Rate, and an Efficiency measure. A single-trade dependence check and a configurable A+ to F grade turn these into clear, decision-ready feedback.
The Maximal Information Coefficient: Detecting Any Relationship, and the Null That Decides Whether It Is Real
This article implements the Maximal Information Coefficient (MINE) for MQL5, including the grid search with dynamic programming and the four MINE statistics. It explains why raw MIC has a nonzero noise floor and builds a permutation null to judge significance. The result is a verified library with a dependence scanner and a chart indicator, allowing you to test features and interpret scores consistently across relationship shapes.
Ollivier-Ricci Curvature: Reading the Shape of a Correlation Network, Not Its Level
The article builds an Ollivier–Ricci curvature library in MQL5 for multi‑symbol analysis. A basket becomes a correlation network, and the reading captures network geometry rather than correlation level. It includes an exact optimal transport solver with an internal certificate, a rolling fragility metric with two informative nulls, an indicator that plots the reading against its null band, and a demonstration expert that uses it as a risk gate.
Forecast Reconciliation (MinT): One Engine for Timeframe Hierarchies and Currency Graphs
This article builds forecast reconciliation in pure MQL5 and applies it to two structures: timeframe aggregation on one symbol and a currency graph linked by no‑arbitrage. The engine projects base forecasts onto linear constraints to make them coherent. We benchmark OLS/WLS and MinT with and without shrinkage on long walk‑forward runs, show when total squared error decreases, and measure the cost that may concentrate in a single node.
Consecutive Loss Streak Analyzer and Risk-of-Ruin Calculator in MQL5
This article presents an MQL5 script that extracts closed trade history, computes empirical win rate and payoff, and evaluates consecutive-loss probabilities using the geometric tail, plus risk of ruin from edge and position size. It plots a CCanvas ruin curve with a live marker at the chosen risk and prints a probability summary, including the account's worst historical streak in theoretical context.
Surrogate Data Testing: A Null Model for Any Statistic, and Why Shuffling Bars Is Not One
We implement surrogate testing for indicators in MQL5: generate synthetic series that match your data's distribution and spectrum, score any statistic, and locate the observation within its null distribution. The library provides four null models, an FFT that handles arbitrary lengths, and a plug‑in interface for custom measures. An indicator visualizes the statistical alongside its chance band for direct interpretation.
Monthly Profit and Loss Calendar Heatmap Renderer in MQL5
The article presents an MQL5 script that reads closed deals, groups them by date, and renders a calendar grid for daily P&L and trade count. It explains the data model, normalization to midnight, robust week/weekday mapping, diverging and single-hue color scales, and CCanvas-based drawing, plus a verification script and weekday summary. This helps you quickly locate clusters and quiet periods and cross-check findings with logged totals.
Price Action Analysis Toolkit Development (Part 86): Validating the Entire Sample Library
This part adds library-wide validation to the double-bottom toolkit. VALIDATE ALL applies the single-sample rule engine to the stored collection, counts its four outcomes and exports a separate CSV report. The report includes settings, sample context and detailed results. Source samples remain unchanged, and export errors are reported separately from completed validation.
Uncertainty as a Model (Part 4): Random Processes — The Dynamics of Uncertainty
The article introduces the concepts and tools for working with random processes in trading: definitions, characteristics, autocorrelation functions, and a practical classification. The article covers white noise, random walks, Wiener and Poisson processes, as well as Markov chains and martingales. MQL5 scripts demonstrate the generation of sample paths and allow you to simulate equity, highlighting the mathematical limitations of strategies.
Recovering Option-Implied Probability Distributions Across Four Markets in MQL5
A practical route from the option chain to probability levels inside MetaTrader 5. For GLD, SLV, SPY, and USO, the risk-neutral density implied by each ETF's options is recovered with the Breeden-Litzenberger identity and checked for static arbitrage, after the method itself is validated against an analytic lognormal. A Python feed publishes the percentiles; an MQL5 service rescales them onto a related symbol, draws levels, and alerts when price leaves the risk-neutral 5 to 95 percent band. Every reading carries its own diagnostics, and full source is included.
Variational Mode Decomposition: Building the Solver, and Measuring What Hindsight Buys
A from‑scratch VMD library for MetaTrader 5: radix‑2 transform, ADMM updates, mirrored windows, and a result type that reports solve quality and mode separation. We verify the solver to full double precision against a reference and test causality by sabotage. The article quantifies repaint from batch versus causal runs and compares it to volatility‑matched random walks. You get a causal indicator, usable diagnostics, and settings that avoid common pitfalls.
Beyond Tick Volume: Measuring Market Activity from the Waits Between Quotes
Tick volume mostly reflects the time of day and is only complete when a bar closes. We build a per‑quote, live activity gauge from the waits between quote changes, remove the intraday rhythm, and model the remainder with the autoregressive conditional duration (ACD) model. We then test whether this activity measure improves short‑horizon volatility forecasts once live price volatility is already in the model.
MetaTrader 5 Machine Learning Blueprint (Part 23): Feature Screening
Permutation tests that assume exchangeable observations miscalibrate feature screens for overlapping financial labels, yielding a tenfold false‑positive inflation on EURUSD. This article implements a calibrated three‑gate pipeline: ADF+KPSS for stationarity, uniform‑grid entropy with modal occupancy, and mutual information corrected via a joint permutation null and Westfall–Young max‑T. The ScreeningReport summarizes gate outcomes and effective test count so you can filter features reliably before fitting models.
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.
Adaptive Trade Management in MQL5: Building a Broker-Aware, Deterministic, and Explainable Exit Engine
This article presents an MQL5 trade-management engine that converts exit rules into proposal generators. A policy engine ranks all proposals by a configurable reason priority with documented tie-breakers. A broker-aware validator checks the candidates in that order and falls back to the next one on rejection, and an execution adapter sends the first accepted request. Reconciliation confirms the result on the position before the internal state changes. The engine uses R-multiples for thresholds, persists intratrade state, and records a decision trace for each managed position on every tick.
Online False Discovery Rate Control: Putting an Error Budget on a Live Signal Stream
The article addresses online false discovery rate control for streaming signals, where fixed thresholds inflate noise discoveries. We port LORD3, LORD++ and SAFFRON into MQL5, construct a causal bootstrap p‑value source without a resolution floor, and verify correctness before market data. Dependence stress tests, a budget/level indicator and a two-arm Strategy Tester show how to configure, monitor and throttle streams to keep the acted-on noise fraction within target.
The MQL5 Standard Library Explorer (Part 17): Building a Reusable Portfolio Manager with CArrayObj
We present a multi‑symbol EA structure that moves symbol‑specific state into independently initialized CStrategyNode objects and manages them with CPortfolioManager. Using CArrayObj with FreeMode, Add(), At(), Delete(), Total(), and Clear(), the manager ensures safe ownership and isolation, while timer‑driven routing and completed‑bar gates keep processing deterministic. This lets you scale portfolios, control risk per node, and avoid duplicated event handling.
Adaptive Trade Management in MQL5: Building a Broker-Aware, Deterministic, and Explainable Exit Engine
This article presents an MQL5 trade-management engine that converts exit rules into proposal generators. A policy engine ranks all proposals by a configurable reason priority with documented tie-breakers. A broker-aware validator checks the candidates in that order and falls back to the next one on rejection, and an execution adapter sends the first accepted request. Reconciliation confirms the result on the position before the internal state changes. The engine uses R-multiples for thresholds, persists intratrade state, and records a decision trace for each managed position on every tick.
Nonlinear OHLC Features Derived from Elliptic Curves
The article discusses the projection of EURUSD daily candlesticks onto the secp256k1 elliptic curve and the extraction of 96 features (EC+TA) to predict the direction of the next candlestick in CatBoost. The price mapping to the curve and the training pipeline on 2,000 D1 bars are shown; the full model achieves a test AUC of 0.6508, with EC features contributing 60.6%. The materials are suitable for reproduction in Python/MetaTrader 5.
Agent Based Market Simulation: Growing a Market From Rules, and Using It to Catch an Overfitted Strategy
A compact MetaTrader 5 library builds a synthetic market from agents: a minority game, a zero‑intelligence double auction, a stylized‑facts analyzer, and a parameter scanner. The result is a testbed with known answers, providing the control real price backtests lack. Each result is cross‑checked by the model's phase transition, a matching Python implementation, and detection of a planted edge.
The MQL5 Standard Library Explorer (Part 17): Building a Reusable Portfolio Manager with CArrayObj
We present a multi‑symbol EA structure that moves symbol‑specific state into independently initialized CStrategyNode objects and manages them with CPortfolioManager. Using CArrayObj with FreeMode, Add(), At(), Delete(), Total(), and Clear(), the manager ensures safe ownership and isolation, while timer‑driven routing and completed‑bar gates keep processing deterministic. This lets you scale portfolios, control risk per node, and avoid duplicated event handling.
Online False Discovery Rate Control: Putting an Error Budget on a Live Signal Stream
The article addresses online false discovery rate control for streaming signals, where fixed thresholds inflate noise discoveries. We port LORD3, LORD++ and SAFFRON into MQL5, construct a causal bootstrap p‑value source without a resolution floor, and verify correctness before market data. Dependence stress tests, a budget/level indicator and a two-arm Strategy Tester show how to configure, monitor and throttle streams to keep the acted-on noise fraction within target.
The Hypothesis of Randomness: Searching for Hidden Patterns in Price Series
The article describes a test of the hypothesis of randomness for quotes based on a chi-square statistic derived from the frequencies of overlapping s-chains. The article shows how to define discrete states and compare observed and expected frequencies in order to detect Markov memory in price increments. This approach helps distinguish structural dependence from noise and formalize the testing of trading hypotheses.