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4.3 KiB
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139 lines
No EOL
4.3 KiB
Markdown
Article-20589-Volatility-Modeling-And-Forecasting-In-MQL5
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## Overview
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This project documents and organizes the concepts presented in an MQL5 article about a native library for univariate volatility modeling and forecasting. The article describes a modular framework inspired by Python's `arch` package, where a complete model is composed of:
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- a mean process,
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- a volatility process,
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- an error distribution.
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The implementation centers on a mean-model base class (`HARX`) that manages initialization, parameter estimation, simulation, and forecasting for the full model.
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## Original Article
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- Article title: Volatility Modeling and Forecasting in MQL5
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- Article ID: 20589
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- Author: Francis Dube
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- Publication date: 2026.01.14
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- Category: Articles / MQL5 programming / optimization / quantitative finance
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- URL: https://www.mql5.com/en/articles/20589
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## Repository Purpose
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This repository should be treated as a reference or reconstruction project based on the article text.
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Its purpose is to capture:
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- the described library architecture,
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- the exposed data structures and APIs,
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- the fitting and forecasting workflow,
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- the ARCH-LM diagnostic procedure,
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- the included demonstration of HAR equivalence via ARX with exogenous averages.
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## Key Concepts
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- Modular volatility modeling in MQL5
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- Mean/volatility/distribution separation
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- `ArchParameters` as a unified configuration struct
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- `ArchModelResult` and `ArchForecast` as result containers
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- HAR, HARX, AR, and ARX mean processes
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- Constant variance, ARCH, and GARCH-family process selection
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- Joint parameter estimation through `fit()`
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- Forecast generation via analytic, simulation, or bootstrap methods
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- Residual diagnostics using Engle's ARCH-LM test
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- Equivalence of HAR and ARX under averaged exogenous regressors
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## Algorithm / Architecture Summary
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The article describes a class hierarchy where `HARX` acts as the base interface for mean models and also orchestrates the full volatility model.
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### Model composition
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A model is formed from three components:
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1. Mean process
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2. Volatility process
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3. Error distribution
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The mean process is the central object and owns the estimation workflow.
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### Configuration
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Model setup is performed through an `ArchParameters` struct, which includes:
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- sample observations,
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- optional exogenous regressors,
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- lag specification,
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- mean model selection,
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- volatility model selection,
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- distribution selection,
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- holdout and scaling options,
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- GARCH order parameters,
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- bootstrap settings,
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- distribution initialization parameters,
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- RNG seeds.
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The `initialize()` method validates and normalizes these inputs, adjusts incompatible options where possible, builds lag matrices, and instantiates the selected volatility process and distribution.
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### Estimation
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The article states that estimation uses ALGLIB's nonlinear constrained optimization via `CMinNLC`, minimizing a log-likelihood objective exposed by the model class.
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The returned `ArchModelResult` includes:
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- estimated parameters,
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- in-sample conditional volatility,
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- residuals,
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- covariance matrix,
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- fit range,
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- log-likelihood,
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- R-squared and adjusted R-squared helpers,
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- t-values, p-values, and standard errors.
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### Forecasting
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Forecasts are returned in an `ArchForecast` struct with:
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- `mean`
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- `variance`
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- `residual_variance`
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The article describes support for:
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- analytic forecasts,
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- Monte Carlo simulation forecasts,
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- bootstrap forecasts.
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For models with exogenous variables, future exogenous matrices must be supplied.
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### Validation
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Model adequacy is checked using `archlmtest()`, which performs a regression-based ARCH-LM test on squared residuals, optionally using standardized residuals. The result is encapsulated in `WaldTestStatistic`, providing:
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- test statistic,
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- degrees of freedom,
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- null and alternative hypotheses,
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- p-value,
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- chi-square critical values.
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### Explicitly attached files in the article text
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- `MQL5/scripts/HAR_as_ARX_Demo.mq5` — demonstration script comparing HAR and ARX formulations
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## Tags
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`mql5`, `volatility-modeling`, `arch`, `garch`, `har`, `arx`, `econometrics`, `time-series`, `forecasting`, `alglib`
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## Difficulty
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Advanced
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## Reference
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- MQL5 article: "Volatility Modeling and Forecasting in MQL5"
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- Demonstrated script: `HAR_as_ARX_Demo.mq5`
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- Related concepts referenced in the article:
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- Python `arch` package
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- ALGLIB `CMinNLC`
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- Engle's ARCH-LM test |