Articles on data analysis and statistics in MQL5

Build a responsive session volume profile indicator in MQL5 from tick data with draggable session bounds and dual anchoring. The article details hash-based bucket aggregation for historical and live ticks, a timer-driven rendering loop with partial updates, automatic or custom bucket sizing, pixel-anchored proportional bars, POC highlighting, and multi‑instance safety—so you can implement, optimize, and run multiple profiles on one chart without UI lag.

This work delivers an MQL5 Expert Advisor that reads open-position symbols, builds return series, and computes a rolling Pearson correlation matrix, displayed as a CCanvas heatmap. Off-diagonal pairs that meet a warning threshold are bordered for quick scanning. The code details return processing, correlation arithmetic, and matrix indexing, with a verification script, helping you track shifting co-movements across your active book.

This part of the series examines the mechanisms of the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) as the theoretical foundation for understanding market patterns. This section describes the tools of descriptive statistics and methods for finding point and interval estimates of distribution parameters. Particular attention is paid to the methodology for testing statistical hypotheses, which makes it possible to objectively distinguish genuine market anomalies from random noise. Each theoretical concept is accompanied by a practical example in the appendix, which helps reinforce the material using specific data.

We introduce a Partial Information Decomposition library for MQL5 that decomposes two sources about a target into four atoms: unique to each, shared, and synergy. The implementation uses quantile binning, tabulated logarithms, and a maximum-entropy fit (for I_ccs), and it pairs results with a block-permutation null because atoms sit above zero on finite samples. Use it to screen indicator pairs and judge significance, including family-wise correction.

This article applies the Kelly criterion to position sizing in native MQL5. It presents a reusable CKelly class that estimates win rate and payoff from closed deals, derives the Kelly fraction, and sizes lots from a stop distance. A Monte Carlo sweep of the Kelly multiplier shows growth peaking at full Kelly while drawdown and ruin increase, motivating fractional Kelly such as half Kelly that preserves most growth with materially lower drawdown.

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.

This article presents a native MQL5 implementation of the ZeroMQ Message Transfer Protocol (ZMTP) built on raw MQL5 sockets. It explains the REQ/REP pattern via the CZmqReqSocket class, including framing, handshake, and strict send/receive alternation. A practical pipeline shows an MQL5 script streaming returns to a Python/R server running MS‑GARCH and receiving regime probabilities, enabling integration without DLLs.

We implement a Time Series Shapelet library for MQL5 that finds the subsequence of price history whose z-normalized shape best separates two labels and derives the decision threshold from information gain. Because candidate searches on prices always return a winner, the fit includes a purged hold-out and a calibrated block permutation null. You get a reusable facade and rules you can plot and evaluate against an explicit noise floor.

Flat files work well at the start of an MQL5 research pipeline, but they hinder cross-run queries and provenance once the archive grows. We build a Python-based SQLite registry that ingests CSV exports with SHA-1 deduplication, records EA version and run timestamps, applies forward-only schema migrations, and indexes common filters. You get a structured query layer for fast lookups, robustness checks, and version comparisons across all campaigns.

We present an MQL5 script that converts closed trade history into comparable metrics: expectancy in currency, pips, and R-multiples, plus a sample-aware win rate via the Wilson interval. These inputs form a conservative, dimensionless Trade Quality Score. The tool draws a CCanvas panel, prints an Experts-tab report, and supports an hour-based session filter to analyze a defined trading window alongside full-history results.

In this article, I will show you, dear reader, how to select the objects we create on the chart and modify the position indicator so that it can perform many more functions than originally intended. We will look at how to implement the ability to move price levels and create price lines directly on the chart. Many people may find this difficult. However, you will see that we'll do this with minimal effort. You just need to give it a little thought.

We show that nested cross-validation removes optimistic evaluation bias but does not stop hyperparameter search from overfitting a finite sample, and we add a diagnostic for when the criterion cannot resolve candidates from noise. We implement OffsetPurgedKFold (boundary-shifted repartitioning), a criterion variance audit (resolution ratio and selection stability), a selection optimization curve, a corrected one-standard-error rule, noise-floor early stopping, and an effective trial count for correlated trials. The result is a dispersion report per candidate and an effective count for the Deflated Sharpe Ratio.

This article implements the scalar Kalman Filter for price smoothing in MQL5 using the standard local-level model and the exact prediction–update equations. It explains how process and measurement noise (Q, R) shape the Kalman gain, builds two independently configured filters into a fast/slow crossover, and provides a complete indicator and Expert Advisor that trade a stability-confirmed signal via iCustom, giving a reproducible baseline for testing and tuning.

We analyze why ratings may be inflated due to the alignment of algorithm trajectories with benchmark diagonals, and we supplement the testing methodology with a requirement to keep the global extremum away from the diagonals. We update Forest and Megacity, and perform RAW verification and calibration using VerifyExtremes.mq5. A drop in HHO and DOAm performance serves as a practical indicator of false leaders.

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.

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.

In the "Every tick based on real ticks" mode, the Strategy Tester's journal reports the minutes for which real ticks were absent or discarded and says that every tick generation was used for them. We show where the journal records this, measure how far back usable tick history goes on two demo servers, and check the ticks from inside an Expert Advisor, so a test range can be chosen by its real-tick share.

Volatility arrives in clusters: one large move makes the next large move more likely, and quiet spells stay quiet. This article builds a Hawkes self-exciting point process in pure MQL5 to measure that effect directly, ending in a single number, the branching ratio, that says how reflexive a market currently is. You get a small, tested library, an indicator that plots the fitted intensity live, and a demonstration Expert Advisor, along with the honest limits of all three.

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.

In this article, I will present our system for simulating market operations. Although everything is practically finished, there are still a few things to implement and a few changes to make. However, I have to admit that, after everything we've already developed, I'm tired of still being stuck on implementing this system.

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.

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.

One of the issues that bothered me the most was that the `C_ElementsTrade` class contains code for accessing positions. Don't take this as a mistake, because it really isn't one. However, this increases the risk of errors in some of the tasks we will need to handle later. All work on implementing the position indicator was carried out with a view to its use in the replay/simulation service. However, when running in this environment, we will have no access to actual positions. Consequently, any call to the MQL5 library intended to retrieve position data will have no effect in this environment.

We turn eigenvalues from a covariance matrix into a normalized spectral‑entropy score that measures how evenly variance is spread across factors. SpectralEntropyCalculator.mq5 compares two portfolios in one run, using native vector summation, ArraySort()-based ordering, element‑wise division, and the Shannon entropy formula. The report makes dominant factors visible and enables quick, repeatable checks of diversification quality.

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.

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.