Articles on data analysis and statistics in MQL5

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.

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.

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.

Part 9 adds a second measurement layer to Part 8's micro‑trend signal: pullback quality. It maps Fibonacci retracement depth to a six‑level PULLBACK QUALITY label, adds an H1 range position from a 60‑bar rolling proxy, and uses lag‑1 momentum autocorrelation. These inputs form a single composite entry‑quality score in [0,1] for filtering setups and sizing trades within MicroStructure_Foundation.mqh.

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.

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.

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.

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.

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.

The second part of the series examines the mathematical framework for multivariate random variables, which is necessary for analyzing the dependence and joint behavior of market assets. This section describes joint distribution functions, the concepts of marginal and conditional distributions, and the conditions for dependence and independence of variables. The theoretical material is based on extending the analogy between probability and mass to multidimensional space. Particular attention is given to measures of association: from classical linear covariance and correlation to modern tools such as copulas and Shannon mutual information.