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.
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 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.
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.
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.
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.
Community of Scientists Optimization (CoSO): Practice
We resume the topic of optimization by the scientific community. CoSO should not be viewed as a ready-made solution, but as a promising research platform. With proper development, CoSO can find its niche in tasks where adaptability and resilience to change are important, and computation time is not critical.
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.
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.
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.
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.
Quantum Neural Network in MQL5 (Part II): Training a Neural Network with Backpropagation on ALGLIB Markov Matrices
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.
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.
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.
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.
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.
Community of Scientists Optimization (CoSO): Practice
We resume the topic of optimization by the scientific community. CoSO should not be viewed as a ready-made solution, but as a promising research platform. With proper development, CoSO can find its niche in tasks where adaptability and resilience to change are important, and computation time is not critical.
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.
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 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.
Quantum Neural Network in MQL5 (Part III): A Virtual Quantum Processor Based on Qubits
The article focuses on creating a trading system with a real quantum simulator instead of mathematical analogies. The system uses 3 virtual qubits, quantum gates and superposition principles to analyze markets. It is implemented as a trading EA for MetaTrader 5 in MQL5. The main achievement is the transition from simulation to real quantum principles of financial information processing.
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.
Artificial Atom Algorithm (A3)
The article describes implementation of the A3 algorithm - a metaheuristic optimization method inspired by chemical processes - in MQL5. Only two adjustable parameters, compactness and a small population, ensure high operating speed with sufficient quality of solutions.