Competitive Learning Algorithm (CLA)
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.
Integrating MQL5 with Data Processing Packages (Part 9): Entropy-Based Adaptive Volatility
This work presents an end-to-end pipeline: collect MetaTrader 5 data, engineer entropy/volatility/trend features, train a PyTorch classifier, and expose predictions through a Flask API. An MQL5 EA posts rolling prices each tick, receives probability and regime, and applies adaptive position sizing and stop distances. The result is a clear recipe for integrating ML inference with MetaTrader 5.
Beyond GARCH (Part IV): Partition Analysis in MQL5
In this article, we shift from Python research to native MQL5 engineering. We build the first module of the MMAR library: a shared constants header, an SVD-based OLS regression class, a Generalized Hurst Exponent estimator, and the partition analysis engine that computes the partition function, extracts tau(q), estimates H via zero-crossing interpolation, and scores multifractality through three diagnostic tests. Tested on 500,000 bars of EURUSD M10, the engine correctly classifies the data as multifractal in under four seconds. Part 4 of an eight-part series. Part 5 fits the tau(q) curve to four candidate distributions via the Legendre transform.
Downloading International Monetary Fund Data Using Python
Downloading international monetary fund data in Python: Mining IMF data for use in macroeconomic currency strategies. How can macroeconomics help an ordinary and an algorithmic trader?
Building an Object-Oriented ONNX Inference Engine in MQL5
This article shows how to run Python-trained models natively in MetaTrader 5 via the terminal's ONNX functions. We build an MQL5 class that encapsulates session creation, fixes input/output tensor shapes, applies min-max feature normalization to mirror training, and executes OnnxRun once per bar to protect the CPU, the result is a reliable, maintainable inference path for live charts and the Strategy Tester without sockets or DLLs.
Kohonen Self-Organizing Maps in an MQL5 Expert Advisor
Kohonen's self-organizing maps transform the chaos of market data into an ordered two-dimensional map, where similar patterns are grouped together. The article demonstrates a complete implementation of a SOM in an MQL5 Expert Advisor with 400 neurons and continuous learning. We break down the Best Matching Unit search algorithm, weight updates using a Gaussian neighborhood function, integration with quantum effects, and the generation of trading signals. The code is open-source, the math is clear, and the results are verifiable.
Defining your Edge (Part 2): Using Divergence Mapping and a Temporal Fusion Transformer in a Trading Robot
In this article we make the case for merging Divergence Mapping with a Temporal Fusion Proxy in a Trading Robot. Rather than depending on lagging price confirmations, the Divergence Mapping's thesis is that acting like a structural sensor can help identify hidden momentum shifts from price action and indicator anomalies. To establish how these anomalies are interpreted over time we use a Temporal Fusion Transformer proxy. This network incorporates historical context to weigh developing trends such that merging it with Divergence Mapping should set us up to spot shifts in accumulation and distribution before price breakouts.
Feature Engineering for ML (Part 10): Structural Break Tests in MQL5
We port AFML Chapter 17 structural break tests to MQL5 as a single include, CStructuralBreaks, delivering six bar-indexed features for EAs: CSW statistic and critical value, Chow-Type DFC, SADF with a rolling lookback (default 252), SM-Exp, and SM-Power. SADF uses O(L²) rolling windows for real-time viability. A companion StructuralBreaksViewer indicator plots all series with per‑series visibility and optional z‑score normalization. SB_EMPTY marks invalid values for safe integration.
Foundation Models for Trading (Part I): Porting Kronos to Native MQL5
Kronos is a pretrained transformer that models OHLCV bars the way a language model predicts words. We reimplement its tokenizer/encoder and transformer block in native MQL5, export weights to flat .bin files, and remove Python from runtime entirely. Part 1 delivers preprocessing and BSQ tokenization plus a bit-for-bit verification harness against PyTorch, so you can run the encoder inside MetaTrader 5 with confidence.
Neural Networks in Trading: Hierarchical Skill Discovery for Adaptive Agent Behavior (HiSSD)
In this article, we explore the HiSSD framework, which combines hierarchical learning and multi-agent approaches to create adaptive systems. We examine in detail how this innovative methodology helps uncover hidden patterns in financial markets and optimize trading strategies in decentralized environments.
Beyond the Clock (Part 2): Building Runs Bars in MQL5
We implement tick-, volume-, and dollar-runs bars in Python and MQL5 and align them with the existing bar‑building framework. The article details the dual‑accumulator update, offline calibration with per‑side seeds, state persistence for EAs, and parity verification to match Python and MQL5 outputs. Runs bars expose one‑sided bursts that net imbalance can hide, improving coverage during quiet sessions and for mean‑reversion models.
Joint Recurrence Quantification Analysis (JRQA) in MQL5: Detecting Simultaneous Recurrence in Two Series
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.
Beyond GARCH (Part VIII): The MMAR Library And Putting it to Work in an Expert Advisor
This article finalizes the MMAR project with a CMMAR facade class and a demo Expert Advisor for MetaTrader 5. The facade exposes a compact API—configure, Fit(), Forecast()—that wraps partition analysis, spectrum fitting and Monte Carlo simulation. You will learn how to load data, fit the model and obtain a volatility forecast, with diagnostics and status handling for robust use in EAs.
Beyond GARCH (Part III): Building the MMAR and the Verdict
With the multifractal parameters from Part 2 in hand, this article builds the full MMAR process. We construct the multiplicative cascade for trading time, generate Fractional Brownian Motion via Davies-Harte FFT, and combine both into X(t) = B_H[theta(t)]. A 100-path Monte Carlo simulation produces the volatility forecast, which we then pit against GARCH on the same EURUSD M5 data. Does Mandelbrot's fractal architecture outforecast Engle's conditional variance framework? Part 3 of a eight-part series leading to a native MQL5 library and Expert Advisor.
MQL5 Wizard Techniques you should know (Part 97): Using Convex Hull and a miniature GRU Network in a Custom Trailing Stop Class
For this article we look at a custom MQL5 Wizard class for Trailing Stops. Our implemented custom class ‘CTrailingConvexHullGRU’, is built from merging the Convex Hull algorithm with a GRU network. As always we seek to develop a model that is testable with MQL5 Wizard-Assembled Expert Advisors and can be tuned with various Money Management and entry Signals classes. Our testing is with the 'Envelopes' and the RSI classes for Signal.
MQL5 Wizard Techniques you should know (Part 100): Sliding Window Median and Bidirectional LSTM for a Custom Trailing Stop
CTrailingSlidingMedianBiLSTM is a custom MQL5 Wizard trailing module that combines robust median/MAD outlier filtering with a BiLSTM context score in the range [-1, 1]. Four algorithm modes (standard, bands, RSI, adaptive) target noise, mean-reverting bursts and liquidity spikes, reducing premature stop adjustments. This module is intended for side-by-side evaluation with diverse entry signals and money management settings.
Neural Networks in Trading: Effective Feature Extraction for Accurate Classification (Building Objects)
Mantis is a versatile tool for in-depth time series analysis that can be flexibly scaled to accommodate any financial scenario. Learn how a combination of patching, local convolutions, and cross-attention enables a highly accurate interpretation of market patterns.
MetaTrader 5 Machine Learning Blueprint (Part 18): Sequential Bootstrap, Corrected — Clone, Class Erasure, and the Comparison Toolkit
The article diagnoses two defects that neutralize sequential bootstrap during cross‑validation: type erasure of SequentiallyBootstrappedBaggingClassifier and a fold‑level shape mismatch from cloning full samples info sets. It retains the classifier's identity, adds find seq bagging to re‑inject fold‑sliced t1 in CalibratorCV.fit, and resets state per split. A new bootstrap_comparison module reports OOF and OOB metrics and memory, letting you verify that sequential sampling is applied correctly and quantify its impact.
Measuring What Matters (Part 1) : Portfolio Risk Decomposition in MQL5
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.
MQL5 Wizard Techniques you should know (Part 98): Using an Unscented Kalman Filter and a Capsule Network in a Custom Signal Class
This article presents 'CSignalUKFCapsNet', as a custom class coded in MQL5. This class is meant to be used with the MQL5 Wizard when assembling an Expert Advisor and when selected in the Wizard it defines the Expert Advisor's entry signals. In building this custom class, we brought together the algorithm Unscented Kalman Filter and the Capsule Neural Network. Our algorithm is showcased with four operation modes, and the coding of this as a custom class for the MQL5 Wizard, allows testing with various Trailing Stop methods and Money Management systems.
Neural Networks in Trading: An Intelligent Forecast Pipeline (Time-MoE)
We invite you to explore the modern Time-MoE framework, which has been adapted for time series forecasting tasks. In this article, we will implement the key components of the architecture step by step, providing explanations and practical examples along the way. This approach will allow you not only to understand how the model works, but also to apply those principles to real-world trading scenarios.
Neural Networks in Trading: Anomaly Detection in the Frequency Domain (Final Part)
We continue to work on implementing the CATCH framework, which combines the Fourier transform and frequency patching mechanisms, ensuring accurate detection of market anomalies. In this article, we complete the implementation of our own vision of the proposed approaches and test the new models on real historical data.
Feature Engineering for ML (Part 11): Fractal Features in Python
The article examines a Williams five‑bar fractal feature pipeline and shows how a centered rolling window creates a true look‑ahead leak. It identifies two additional silent bugs—a hardcoded shift tied to the default n and a volatility threshold that ignores its input—and consolidates fixes under a single leak_safe flag. Readers get leak‑free fractal, level, trend, and signal features, plus guidance on when unshifted columns remain valid for labeling.
Recurrence Network Analysis (RNA) in MQL5: From Recurrence Matrices to Complex Networks
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.
MetaTrader 5 Machine Learning Blueprint (Part 19): Bagging Regimes
We test AFML's claim that the sequential bootstrap decorrelates bagged trees on overlapping triple‑barrier labels by isolating two levers: draw count and draw rule. One decision identical tree is bagged under four row‑sampling regimes and evaluated on EURUSD 2022–2023 for draw uniqueness, between‑tree correlation, AUC, and calibration. Decorrelation comes almost entirely from throttling max_samples to average uniqueness; the sequential draw adds little. Out-of-bag inflation is largest under full-count sequential sampling.
MQL5 Wizard Techniques you should know (Part 91): Using Skip Lists and a Hopfield Network in a Custom Trailing Class
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.
Beyond the Clock (Part 4): Efficacy of Bars on Trending and Mean-Reversion Strategies
Does better return conditioning buy strategy performance? We hold bar count fixed across time, tick, tick-imbalance, and tick-runs on 60.5 million EURUSD ticks, then meta-label RSI, Bollinger, and ADX/DI entries and score with purged cross-validation. No family delivers a consistent edge; efficacy varies narrowly and the best case fails a permutation test. Readers learn how to control overlap, leakage, and multiple testing in bar studies.
Neural Networks in Trading: Effective Feature Extraction for Accurate Classification (Final Part)
The Mantis framework transforms complex time series into informative tokens and serves as a reliable foundation for an intelligent trading agent capable of operating in real time.
Measuring What Matters (Part 2): Building the Covariance Matrix: Eigenvalue Decomposition and Risk Factor Analysis in MQL5
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.
MCMC Sampling Methods — The Metropolis-Hastings Algorithm
The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method that is widely used to approximate posterior distributions in Bayesian inference. This article describes the theoretical foundations of the algorithm, the implementation of the MHSampler class in MQL5, and examples of its application, including an analysis of the resulting samples.
MCMC Sampling Methods: The Slice Sampling Algorithm
The article examines slice sampling — an adaptive MCMC algorithm that automatically adjusts its sampling parameters. Its effectiveness is demonstrated using Bayesian linear and logistic regression models, and the results are compared with classical frequentist methods.
Beyond GARCH (Part V): Fitting the Multifractal Spectrum in MQL5
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.
Analysis of the Impact of Solar and Lunar Cycles on Currency Exchange Rates
What if lunar cycles and seasonal patterns influence the foreign exchange markets? This article shows how to translate astrological concepts into the language of mathematics and machine learning. I built a Python system with 88 features based on astronomical cycles, trained CatBoost on 15 years of EURUSD data, and obtained some intriguing results. The code is open-source, the methods are verifiable, and the conclusions are unexpected — ancient wisdom meets gradient boosting.
Porting the Canonical Catch22 Time-Series Feature Set and Testing It on Volatility Regimes
We present a native MQL5 implementation of the catch22 feature set: all 22 canonical time-series characteristics in a reusable class validated against pycatch22. Using a leak-free pipeline (chronological split, purging, embargo), we run a three-arm ablation—classic indicators, catch22, and combined—for volatility-regime classification. Finally, we deploy the combined model as a Strategy Tester regime filter to quantify its impact on a simple baseline strategy.
Neural Networks in Trading: An Intelligent Forecast Pipeline (Sparse Mixture of Experts)
We invite you to explore the practical implementation of a sparse mixture of experts block for time series in the OpenCL computing environment. This article provides a step-by-step explanation of how masked multi-window convolution works, as well as how gradient-based training is organized in the presence of multiple information streams.
Beyond GARCH (Part VI): Fractional Brownian Motion And The Multiplicative Cascade in MQL5
This article implements the MMAR Simulation Engine that turns fitted parameters (H, distribution, coefficients, sample volatility) into synthetic price paths. It builds multifractal trading time via a multiplicative cascade, synthesizes fractional Brownian motion with Davies–Harte or Cholesky, scales it to target volatility, and composes the process by time deformation. Readers get a reusable MQL5 class, method choices by path length, and validation steps for scenario testing and Monte Carlo use in the next part.
MQL5 Wizard Techniques you should know (Part 99): Using a KD-Tree and an Echo State Network in a Custom Money Management Class
This article lays out 'CMoneyKDTreeESN' custom money management class usable with the MQL5 Wizard, that combines the KD-Tree algorithm and the Echo State Network. We use the KD-Tree on log returns and ATR to give us a risk score, while the ESN tracks recent flow to give us a bounded lot size multiplier. Our class is usable in a variety of Wizard assembled Expert Advisors as shown here with the Envelopes and RSI signals, with a broad objective of modulating exposure in high-volatility and tail-risk environments.
MQL5 Wizard Techniques you should know (Part 94): Using Reservoir Sampling and Linear Regression in a Custom Trailing Stop Class
For this article we rotate to a custom MQL5 Wizard class implementation that explores Trailing Stops. Our custom class is ‘CTrailingReservoirLinReg’ that we derive by combining the Reservoir Sampling algorithm with a Linear Regression network. As has been the case throughout these series, this formulation is testable with MQL5 Wizard Assembled Expert Advisors that can be tuned with various entry signals and money management classes.
From One Price to Four: Range-Based Volatility Estimators for MetaTrader 5
Close-to-close volatility ignores the high, the low, and overnight gaps. We build a reusable MQL5 library implementing four range-based estimators from Parkinson to the gap-robust Yang-Zhang, and put it to work in a comparison indicator and a set of adaptive volatility bands.
MQL5 Wizard Techniques you should know (Part 96): Using Wavelet Thresholding and LSTM Network in a Custom Money Management Class
In this article we consider a custom MQL5 Wizard class that processes Money Management. Our custom class is labelled ‘CMoneyWaveletLSTM’, and is developed by combining the Wavelet Thresholding algorithm with an LSTM network. As has been the case throughout these series, the developed model is testable with MQL5 Wizard-Assembled Expert Advisors that can be tuned with different trailing stops and entry Signals classes. We maintain our entry Signal, as in past articles as the built-in 'Envelopes' class and the RSI class.