Hammad Dilber / Profilo

This article turns the verified TDA pipeline into a live MQL5 indicator. It reduces each price window to two persistence-entropy lines (H0 and H1), computes a normalized loop-strength metric with an adaptive percentile band, and places fade marks only when loop strength is high and price hits a window extreme. You can attach the indicator, read six buffers from an Expert Advisor, and tune key window, ranking, and performance parameters.

We complete persistent homology for MQL5 by reducing the Vietoris–Rips boundary matrix to a persistence diagram. The article implements Z/2 column reduction (CTDAReduction), a diagram container with analytics (CTDADiagram), and a facade that runs the six-stage pipeline in one call (CTDA). Outputs are cross-checked against Ripser to numerical agreement, enabling reliable diagram-based metrics.

We turn a price-embedded point cloud into a Vietoris–Rips filtration and its boundary matrix. The article enumerates vertices, edges, and triangles with filtration values, sorts them in entry order, and builds O(1) vertex/edge lookups. You get MQL5 classes CTDARips and CTDABoundary and a sparse Z/2 boundary suitable for the next-step persistence reduction.

The article presents a practical foundation for shape analysis of price series in MQL5. It implements Takens time‑delay embedding to build a phase‑space point cloud and computes the full pairwise distance matrix under selectable norms. The CTDAPointCloud and CTDADistance classes are provided with a demo script that embeds chart data and outputs results, preparing inputs for downstream topological tools.

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.

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.

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 builds a complete Recurrence Quantification Analysis (RQA) toolkit for MetaTrader 5 in pure MQL5. We cover phase-space reconstruction, time-delay embedding, distance and recurrence matrix construction, RQA metric extraction, automatic epsilon selection, and rolling-window computation through a modular library design. The article concludes by applying the library in a practical indicator that plots RR, DET, LAM, ENTR, and TREND directly on the chart, providing a solid foundation for nonlinear time-series analysis in MQL5.