Detecting Structural Breakpoints in Price Series Using CUSUM in MQL5 (Part 2): Implementing the Detector as a Native MQL5 Indicator
This article benchmarks CUSUM_Breakpoint.mq5 against the Siegmund ARL₀ prediction on live‑like data. The empirical false‑alarm rate is about five times higher than theory for all tested symbols and timeframes, and confirmations show sensitivity to variance changes over mean changes. Practitioners should calibrate h and k on the target instrument's history and apply the signal to manage volatility regimes, not to infer directional shifts.
Building a Swing-Based Volume Profile Indicator in MQL5
This article presents a swing-based volume profile indicator in MQL5 that analyzes platform tick volume within completed high-to-low and low-to-high legs. It confirms swing points, partitions each leg's range into ATR(200)‑adaptive price bins, distributes tick volume, and marks the Point of Control. The indicator draws a ZigZag and renders the profile on chart rectangles, helping you study volume concentration within each swing relative to price structure.
From Static MA to Adaptive Filtering (Part 1): Introducing SAMA with NLMS in MQL5
This article introduces the Self-Adaptive Moving Average (SAMA), an adaptive filter leveraging the Normalized Least Mean Squares (NLMS) algorithm. It explores why fixed-period averages fail, how NLMS adapts bar by bar, and the engineering protections required for production. This conceptual and mathematical foundation prepares you for the MQL5 code implementation in Part 2.
From Option Chain to 3D Volatility Surface in MetaTrader 5
This article walks through creating an MT5 indicator that ingests option chains from native symbols or CSV, inverts prices to implied volatility via a hybrid Newton–Raphson/bisection method, and assembles a clean strike–expiry grid. It then renders a shaded, rotatable 3D surface with the platform's DirectX layer, enabling clear, in-terminal analysis of skew and term structure using live or file-based data.
Learnable Curves, Not Weights: A Kolmogorov-Arnold Network from Scratch
This article builds a Kolmogorov–Arnold Network (KAN) in MQL5, where every edge carries a learnable B‑spline curve rather than a scalar weight. We construct the spline basis, assemble edges and a layer, and fit all coefficients by ridge‑regularized least‑squares in a single solve. The model is delivered as an indicator that visualizes the learned curves and an Expert Advisor that acts on the prediction, providing an interpretable, reusable codebase.
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.
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.
Rolling Sharpe Ratio with Statistical Significance Bands in MQL5
This article presents a custom MetaTrader 5 indicator that computes a rolling annualized Sharpe ratio and plots configurable z-score significance bands based on Lo's asymptotic standard error. It uses a circular return buffer with incremental variance to keep O(1) updates. We explain the n^(-1/2) uncertainty scaling, the inflation of intervals at high Sharpe values, and how to set per-instrument annualization for correct deployment.
Defining your Edge (Part 3): Using HMM and GRU in an Expert Advisor
We examine how a Hidden Markov Model (HMM) estimates latent market regimes while basing on observable price and indicator sequences. This is done by estimating the probability of state transitions. A Gated Recurrent Unit (GRU) network models time dependencies and keeps important information over several observations. In an Expert Advisor, HMM-based regime probabilities, can be merged with GRU-based sequence learning to better classify increments in accumulation, distribution, and momentum prior to their showing up in regular price confirmations.
Beyond GARCH (Part VII): Monte Carlo Volatility Forecasting in MQL5
We implement the CMonteCarlo module that turns the fitted MMAR parameters into a volatility forecast via Monte Carlo. It runs N independent simulations over a chosen horizon and reports mean, median, standard deviation, and a percentile-based 95% confidence interval, with access to per-run values if needed. Adaptive cascade depth selects the minimal k such that b^k covers the horizon, keeping the run fast and consistent.
Implementing and Benchmarking Bag-of-SFA-Symbols (BOSS) Against Dynamic Time Warping (DTW)
This article implements BOSS from scratch in MQL5 and applies it to regime classification: SFA turns windows into words, bags record word frequencies, and an ensemble over window lengths votes on labels. We cover the encoding steps, the BOSS distance, training with auto-generated regime labels, and practical parameters. A BTCUSD benchmark versus DTW shows higher macro accuracy on clean data and markedly faster inference.
How to Use Finite Differences for Price Forecasting
The article examines the practical application of finite differences in trading: types of differences, their relationship to price dynamics, and the binomial transform for noise filtering. The rules for encoding patterns based on difference levels and the application of these patterns to forecasting are described. This section presents naive, adaptive, and probabilistic approaches that help smooth time series, identify recurring patterns, and estimate future movements.
Feature Engineering for ML (Part 8): Entropy Features in MQL5
An MQL5 port of four entropy estimators — Shannon, Plug-In, Lempel-Ziv, and Kontoyiannis — operating on the intrabar tick-rule sequence. CopyTicksRange() limits data to the broker's cached tick window, so features apply to recent bars only. The implementation encodes bid-direction ticks from MqlTick, replaces NumPy-dependent steps with array-based methods, and ships CEntropyFeatures.mqh and EntropyViewer.mq5 for EA and indicator use.
Isolation Forest: Unsupervised Anomaly Detection, and What It Actually Finds in Price Data
This article implements a self-contained Isolation Forest library for MetaTrader 5 with no labels, no distribution assumptions and no external dependencies. It details a reproducible 64‑bit generator, tree/forest construction, scoring and feature design, then verifies results against Python and market data with two null models. The package includes an indicator that plots the decision variable and a gate example. Readers get a validated library, clear limits of applicability and a practical way to calibrate thresholds.
Building a Market Behavior Analyzer in MQL5
We outline a modular analyzer for MetaTrader 5 that separates detection, interpretation, and visualization. The engine identifies swing highs and lows, assigns structural labels, evaluates impulses and pullbacks, and stores results in a market state object. An on‑chart dashboard and interactive inspection tools make the latest structure and measurements immediately accessible.
MiniRocket: A Deterministic Time-Series Classifier and What It Finds in Seven Classic Setups
This article delivers a native MQL5 MiniRocket: 84 fixed convolution kernels yield 9,996 features quickly and deterministically, requiring no training loop and no external runtime. We verify the port against sktime and a float64 reimplementation, then run a reproducible audit of seven classic setups; planted and coin‑flip controls confirm correctness, and a 25%‑flipped control sets the detection threshold.
Defining your Edge (Part 5): Using GARCH Variance and Volatility-Scaled LSTM in an Expert Advisor
We merge GARCH(1,1) variance projections with ATR plus Bollinger-Bands patterns to form an algorithm that could optionally be used with volatility-scaled LSTM within LSTM Wizard-ready signal class. We cover feature scaling, mode scoring, thresholds, and safety checks. Readers can replicate backtest/forward test results to verify if the recurrent layer gives incremental discrimination over our deterministic baseline.
Symbolic Fourier Approximation in MQL5: Benchmarking SFA Against SAX
We implement Symbolic Fourier Approximation in MQL5 and compare it to SAX under a shared harness on identical price windows. SFA keeps low‑frequency Fourier coefficients and learns per‑position bins (MCB), with a proven, sound lower bound. The measurements show how the same bit budget behaves under different splits of word length and alphabet, and give a practical rule for choosing settings for your symbol.
Building Volatility Models in MQL5: Implementing the APARCH Volatility Process
The article introduces the APARCH volatility process to the MQL5 library via the CAparchProcess class, estimating the power exponent (delta) jointly with other parameters. It details the recursion, parameter bounds, stationarity constraints, and starting values and reports SLSQP solver updates that streamline optimization. Implementation correctness is partially validated by reproducing approximations of GARCH and GJR-GARCH conditional volatility under parameter restrictions. A companion APARCH indicator visualizes conditional volatility, standardized residuals, and delta to track volatility dynamics and parameter drift.
Defining your Edge (Part 4): Applying Isotonic Regression and PNN Price-Forecasting in an Expert Advisor
We consider the methods with which Isotonic Regression calibrates raw RSI, Stochastic and price-action signal scores into probabilities that are sorted, while a separate Probability based Neural Network evaluates similar historical market states. This article uses both approaches in a ready-made MQL5 custom signal class that is compatible with MQL5 Wizard and provides up to 7 selectable entry modes. Reproducible tests compare isotonic-only signals with the combined Isotonic-PNN model to assess whether the network adds useful information beyond the simpler baseline.
Partial Information Decomposition: When Two Indicators Together Say More Than Either Alone
We introduce a Partial Information Decomposition library for MQL5 that decomposes two sources about a target into four atoms: unique to each, shared, and synergy. The implementation uses quantile binning, tabulated logarithms, and a maximum-entropy fit (for I_ccs), and it pairs results with a block-permutation null because atoms sit above zero on finite samples. Use it to screen indicator pairs and judge significance, including family-wise correction.
From Option Chain to Risk-Neutral Density: The Market's Own Probability Distribution
The article builds an MQL5 indicator that recovers the risk-neutral density from an option chain via the Breeden–Litzenberger identity. Quotes are inverted to implied volatilities, the smile is smoothed and priced back to arbitrage‑free calls, and the second derivative yields the density. The tool reports probabilities above any level, the expected move, skew and kurtosis, and overlays the realized-return distribution for comparison.
From Delta-Space Quotes to the FX Volatility Smile: Garman-Kohlhagen and the Convention Problem
FX options are quoted in delta space, not by strike. This article implements an FX-native smile tool for MetaTrader 5: it converts ATM, risk reversal and butterfly quotes into strike-space pillars, prices with the Garman–Kohlhagen model, handles spot/forward and premium-adjusted delta conventions per pair, and draws the smile with a reconstructed strike ladder and Greeks.
Time Series Shapelets: Learning a Price Shape, and Testing Whether It Means Anything
We implement a Time Series Shapelet library for MQL5 that finds the subsequence of price history whose z-normalized shape best separates two labels and derives the decision threshold from information gain. Because candidate searches on prices always return a winner, the fit includes a purged hold-out and a calibrated block permutation null. You get a reusable facade and rules you can plot and evaluate against an explicit noise floor.
Regime Discovery by Structure: Implementing Toeplitz Inverse Covariance Clustering (TICC)
This article presents a full MQL5 pipeline for Toeplitz Inverse Covariance Clustering: stacked observations, ADMM‑based graphical lasso with block‑Toeplitz constraints, and dynamic‑programming regime assignment. It separates structure from volatility and conditions away the shared USD leg. The fitted regimes are displayed causally as a non-repainting ribbon with a dependency graph for the active state.
MiniRocket: A Deterministic Time-Series Classifier and What It Finds in Seven Classic Setups
This article delivers a native MQL5 MiniRocket: 84 fixed convolution kernels yield 9,996 features quickly and deterministically, requiring no training loop and no external runtime. We verify the port against sktime and a float64 reimplementation, then run a reproducible audit of seven classic setups; planted and coin‑flip controls confirm correctness, and a 25%‑flipped control sets the detection threshold.
The Maximal Information Coefficient: Detecting Any Relationship, and the Null That Decides Whether It Is Real
This article implements the Maximal Information Coefficient (MINE) for MQL5, including the grid search with dynamic programming and the four MINE statistics. It explains why raw MIC has a nonzero noise floor and builds a permutation null to judge significance. The result is a verified library with a dependence scanner and a chart indicator, allowing you to test features and interpret scores consistently across relationship shapes.