Articles on data analysis and statistics in MQL5

The article presents the Competitive Learning Algorithm (CLA), a new metaheuristic optimization method based on simulating the educational process. The algorithm organizes the population of solutions into classes with students and teachers, where agents learn through three mechanisms: following the best in the class, using personal experience, and sharing knowledge between classes.

We extend the RQA library for MetaTrader 5 with JRQA, which detects when two series simultaneously revisit their own past states. The article covers the joint recurrence matrix, twelve JRQA metrics (including TREND and COMPLEXITY), dual-epsilon configuration, and a rolling-window engine with OpenCL acceleration and automatic CPU fallback. A practical indicator plots JRR, JDET, JLAM, JENTR, and JTREND for any symbol pair with timestamp alignment and normalization.

Part 2 focuses on practical long-memory detection for intraday data. Three complementary Hurst estimators are implemented and combined into a confidence‑weighted composite, with confidence tied to valid regression scales. The final H and confidence populate the shared analysis struct, enabling indicators to act only when H departs from the neutral 0.40–0.60 band and to select trend‑following above 0.60 or mean‑reversion below 0.40.

This article extends the MQL5 RQA library to Cross-Recurrence Quantification Analysis (CRQA) for comparing two time series. We implement dual‑series embedding, cross‑recurrence matrix construction, adapted metrics (CRR, CDET, CLAM, CENTR, and others), and rolling‑window analysis, with optional GPU acceleration via OpenCL. A ready-to-use indicator compares two symbols in real time, supporting timestamp alignment and normalization for practical inter-market analysis.

This article extends the MQL5 RQA library to Cross-Recurrence Quantification Analysis (CRQA) for comparing two time series. We implement dual‑series embedding, cross‑recurrence matrix construction, adapted metrics (CRR, CDET, CLAM, CENTR, and others), and rolling‑window analysis, with optional GPU acceleration via OpenCL. A ready-to-use indicator compares two symbols in real time, supporting timestamp alignment and normalization for practical inter-market analysis.

For our next Exploration on notions that are testable with the MQL5 Wizard we examine if Skip Lists and the Hopfield Network can give us a profit-guarding trailing strategy. Trailing Stop Management, as already argued, can be overlooked in most trading systems at the expense of Entry Signals or even Money Management. Trailing stops can make all the difference in certain situations such as trending markets, and thus we test this out with GBP USD.

The article presents an innovative quantum neural network architecture for algorithmic trading that combines the principles of quantum mechanics with modern machine learning methods. The system includes quantum effects (resonance, interference, decoherence), multi-level memory of different time scales, Markov chains with the ALGLIB library, and adaptive parameter control. The full implementation is done in MQL5 using the built-in matrix/vector types, which removes implementation barriers in MetaTrader 5.

The article extends the MQL5 recurrence library to Recurrence Network Analysis (RNA) by treating recurrence matrices as adjacency matrices of undirected graphs. It implements core network metrics—clustering, transitivity, average path length, betweenness, assortativity, and density—and applies them in rolling windows for single-series RNA and Joint RNA (JRNA). A modular metrics engine and two indicators visualize the evolving network structure on MetaTrader 5 charts for practical time-series analysis.

Many people tend to underestimate SQL, or even not use it at all, because they do not fully understand how it actually works. When running queries against an SQL database, we are not always looking for a universal answer; in some cases, we need a very specific and practical answer. If a database is created with a proper structure and data model, almost any type of information can be integrated into it.

This article builds the Spectrum Fitter: from tau(q) we compute f(alpha) with a discrete Legendre transform, then fit Normal, Binomial, Poisson, and Gamma spectra under box constraints using BLEIC. The best model by SSE is selected, and its parameters (eg, alpha min, alpha max or alpha_0, gamma) become the cascade inputs for multifractal simulation.

In today's article we will begin studying the use of SQL in MQL5 code. We will also look at how to create a database. Or, more precisely, how to create a SQLite database file using the features built into MQL5. We will also see how to create a table, and then how to establish a relationship between tables by using primary and foreign keys. All of this, once again, will be done with MQL5. We will see how easy it is to create code that can later be migrated to other SQL implementations by using a class that helps hide the implementation being created. And, most importantly, we will see that at various points we may face the risk that something will go wrong when using SQL. This happens because, in MQL5 code, SQL code will always be placed inside a string.

This article adds six order-flow functions and a new OrderFlowAnalysis struct to MicroStructureFoundation.mqh: VPINOHLC, signed flow imbalance, trade intensity versus a 20-session baseline, a late-minus-early smart-money index, flow momentum, and a wrapper that outputs a confidence weight. Flow confidence is gated by noise and jump intensity from Parts 5 and 4. Calibrated on 602 NQ M1 NY sessions, it provides ready-to-use intraday flow signals with documented thresholds.

This article introduces a frequency-analysis framework for encoded candlestick patterns in MQL5. By transforming candlesticks into alphabetic symbols, historical price action can be analyzed as a statistical sequence rather than a visual chart. Using GBPUSD and Gold across multiple timeframes, the study examines the occurrence frequency of individual candlestick types, identifies dominant market structures, and reveals the symmetry between bullish and bearish price movements. The results establish a quantitative foundation for pattern discovery and prepare the way for analyzing multi-candlestick sequences and their predictive potential in algorithmic trading systems.

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.