Articles on data analysis and statistics in MQL5

This article implements a path-dependent volatility model in MQL5 that keeps the sign of returns. The engine uses two-timescale EWMA kernels (four accumulators) to form activity and trend features, with closed-form coefficients and a lightweight kernel search. We provide a calibration workflow and an indicator that plots the decomposition, then test out of sample against EWMA and GARCH on multiple symbols. Results show clear gains on equity indicators and minimal gains on FX.

This article implements the Probability of Backtest Overfitting in MQL5 with Combinatorially Symmetric Cross-Validation. It shows how to build the bar-by-bar returns matrix of a parameter grid, aggregate it by blocks and rank the in-sample winner out-of-sample across every split of the history. You get a single probability that this winner ends up in the lower half of the grid out-of-sample, along with the MQL5 code to compute it on your own optimizations.

The article implements Online Portfolio Selection in MQL5: exact simplex projection, four allocators (EG, Universal Portfolio, PAMR, OLMAR), and a BCRP solver on a concave objective. We verify weight paths against the published Python reference and self-check the optimizer. A drift-aware transaction cost model measures turnover and net wealth on a multi-asset basket. Readers get a tested library and evidence on when regret-bounded methods lose to costs.

We present a multi‑symbol EA structure that moves symbol‑specific state into independently initialized CStrategyNode objects and manages them with CPortfolioManager. Using CArrayObj with FreeMode, Add(), At(), Delete(), Total(), and Clear(), the manager ensures safe ownership and isolation, while timer‑driven routing and completed‑bar gates keep processing deterministic. This lets you scale portfolios, control risk per node, and avoid duplicated event handling.

The article addresses online false discovery rate control for streaming signals, where fixed thresholds inflate noise discoveries. We port LORD3, LORD++ and SAFFRON into MQL5, construct a causal bootstrap p‑value source without a resolution floor, and verify correctness before market data. Dependence stress tests, a budget/level indicator and a two-arm Strategy Tester show how to configure, monitor and throttle streams to keep the acted-on noise fraction within target.

Permutation tests that assume exchangeable observations miscalibrate feature screens for overlapping financial labels, yielding a tenfold false‑positive inflation on EURUSD. This article implements a calibrated three‑gate pipeline: ADF+KPSS for stationarity, uniform‑grid entropy with modal occupancy, and mutual information corrected via a joint permutation null and Westfall–Young max‑T. The ScreeningReport summarizes gate outcomes and effective test count so you can filter features reliably before fitting models.

A practical route from the option chain to probability levels inside MetaTrader 5. For GLD, SLV, SPY, and USO, the risk-neutral density implied by each ETF's options is recovered with the Breeden-Litzenberger identity and checked for static arbitrage, after the method itself is validated against an analytic lognormal. A Python feed publishes the percentiles; an MQL5 service rescales them onto a related symbol, draws levels, and alerts when price leaves the risk-neutral 5 to 95 percent band. Every reading carries its own diagnostics, and full source is included.

An LLM agent with SQL memory in MetaTrader 5 — an architecture that eliminates the main limitation of traditional LLM Expert Advisors (EAs): the loss of context between queries. Each agent decision is recorded in SQLite along with the market conditions at the time of the signal — RSI, MA alignment, volatility — and after the position is closed, the outcome is written to the database. When the next request comes in, the agent reviews its own history — similar past RSI conditions and the last three agent decisions — and only then analyzes the current market. The result is a system that remembers its errors between restarts and adapts its behavior based on accumulated statistics, rather than starting from scratch with each new bar.

The article introduces the concepts and tools for working with random processes in trading: definitions, characteristics, autocorrelation functions, and a practical classification. The article covers white noise, random walks, Wiener and Poisson processes, as well as Markov chains and martingales. MQL5 scripts demonstrate the generation of sample paths and allow you to simulate equity, highlighting the mathematical limitations of strategies.

This part adds library-wide validation to the double-bottom toolkit. VALIDATE ALL applies the single-sample rule engine to the stored collection, counts its four outcomes and exports a separate CSV report. The report includes settings, sample context and detailed results. Source samples remain unchanged, and export errors are reported separately from completed validation.

The framework evaluates boundary sensitivity by rebuilding shifted target-timeframe bars from completed M1 sources and running one Strategy Tester pass for each boundary offset. It includes a ShiftedBarBuilder, a demonstration EA, and a deterministic self-test. An XAUUSD M15 case study reports net profit, Profit Factor, maximum relative equity drawdown, and total trades across all 15 offsets to quantify dependence on the bar grid.

We implement the Harris Hawks Optimization algorithm in MQL5 and analyze five movement modes of agents controlled by a single parameter — the decaying escape energy E. The C_AO_HHO class is introduced; it is compatible with the unified test bench and features a reproducible implementation of Lévy flight. The algorithm was tested on the Hilly, Forest, and Megacity functions with 5, 25, and 500 coordinates — the results indicate anomalous behavior.

The article builds an Ollivier–Ricci curvature library in MQL5 for multi‑symbol analysis. A basket becomes a correlation network, and the reading captures network geometry rather than correlation level. It includes an exact optimal transport solver with an internal certificate, a rolling fragility metric with two informative nulls, an indicator that plots the reading against its null band, and a demonstration expert that uses it as a risk gate.

This work adds an explainable validation module to the recording toolkit for double bottoms. It finds and filters swing lows, selects the neckline, quantifies depth, low similarity, symmetry and recovery, and assigns a rule-based status and scores accepted pairs. The settings are configurable, the process is reproducible, and the original sample data remains intact for comparison across rule sets.