Kayode Michael Oyetunde / Profilo

A complete MQL5 implementation of the Ljung-Box test helps verify independence in trading data and fitted-model residuals. It computes sample autocorrelations, the Q statistic over selected horizons, degrees of freedom with user-controlled adjustments, and right-tail p-values via the regularized incomplete gamma function. Run it on returns, deal outcomes, or external residuals and review decisions directly in the Experts tab.

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.

Net profit and win rate do not tell you if a strategy's edge is statistically real. This MQL5 toolkit analyzes return series built from price data or deal history and reports t‑statistics, p‑values, and confidence intervals using one-sample and Welch t‑tests, the Mann–Whitney U test, and volatility‑regime analysis to support evidence‑based trading decisions.

This article performs a numerical verification of MQL5 eigendecomposition for a covariance matrix using the spectral theorem A = V Λ Vᵀ. It reconstructs the matrix with Diag(), Transpose(), and MatMul(), computes the residual and its Frobenius norm, and shows that deviations remain at floating‑point precision, with results printed to the Experts journal.

In Part 2, we introduce a reusable CCovarianceMatrix class that computes and stores a covariance matrix from raw return series using MQL5's native Cov() method. We verify symmetry, print a labeled matrix grid, and call Eig() to obtain eigenvalues and eigenvectors. Readers see how symbols co-move and which factors drive variance, enabling clearer portfolio diagnostics and reuse in scripts or EAs.

The article establishes a reproducible method to measure portfolio risk for multiple symbols using MQL5 matrices and OpenBLAS. It covers computing log returns, building a covariance matrix, and evaluating wᵀΣw instead of summing individual variances. A complete script prints naive versus true volatility and the cross‑term contribution, enabling you to detect when correlated instruments inflate exposure beyond single‑asset estimates.