Articles on data analysis and statistics in MQL5

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.

In this article, I have shown—in the clearest possible way—how to modify and improve code capable of handling specific tasks while making as few changes as possible to the existing code. We will add a volume display and, at the same time, ensure that users or traders cannot effectively remove objects created by the position indicator.

We consider a BAS+PSO (BSO) hybrid, where BAS provides a local direction signal and PSO facilitates the exchange of best solutions within the swarm. The article presents a mathematical model, pseudocode, an implementation of the class in MQL5, and test results from a standard test bench. This material allows reproducing the algorithm, configuring its parameters, and understanding how three objective-function evaluations per iteration affect efficiency.

In the previous article, we configured the indicator to display the financial result. However, not everyone likes using this display mode. The reasons differ from one trader to another, although in some cases they seem quite reasonable and justified to me. Adapting the code to provide this capability is by no means one of the most difficult tasks. It's actually pretty simple. In this article, we'll look at how to do this.

This article explains Monte Carlo simulation and analysis for trading and guides you through a Python tool that ingests MetaTrader 5 HTML reports. It generates many randomized equity paths, then summarizes them with max drawdown, bust/profit rates, and percentile envelopes around the mean curve. The workflow helps you assess uncertainty, separate normal behavior from outliers, and size positions accordingly.

In this article, we will make the necessary changes so that the position indicator displays the financial result. This way, the trader will be able to get an idea of the financial result of an open position. In addition, I will tell you something that many people do not know, even those who have been using MQL5 for a long time: how to use static variables to share memory and avoid declaring a global variable in the main code.

The article discusses the Colliding Bodies Optimization (CBO) algorithm, which is based on the physics of one-dimensional collisions between bodies. The basic version of the algorithm does not include any configurable parameters, which makes it simple. Therefore, the enhanced ECBO version — supplemented with Colliding Memory and a crossover mechanism — was used as the basis for the implementation, allowing the algorithm to achieve respectable results and earn a place in the ranking table.

Financing drives multi‑day index‑CFD results: in one full‑history test, swap consumed 44% of gross profit and all profit on one symbol. We convert swaps to annualized rates, contrast four brokers and two financing models with a read‑only script, and quantify a Strategy Tester issue where a single current swap is used for all history, inflating implied rates by up to seven times. The piece provides a repeatable cost‑audit method.

The article proposes a hybrid approach to algorithmic trading based on quantum encoding of market states, Double DQN with a prioritized experience replay buffer, and an LLM acting as a contextual EA. The SEAL methodology enables asynchronous continued training of the agent without halting trading. A lightweight Q-learning filter (USE/SKIP/REDUCE) controls signal execution at the meta-level. Practical details are provided on integrating the system with the MetaTrader 5 trading platform, along with a scheme for adapting it to market regime shifts.

In this article, we will implement a number of improvements to ensure that the position indicator accurately reflects the actual state on the trading server in terms of open positions and their current state. I should point out that the applications shown here are in no way intended to replace any of the elements available in MetaTrader 5. They should also not be used without due caution and a balanced approach, since their purpose is to provide educational code—that is, code intended solely for learning how the system works. The reason I call this code “educational” is that, in some cases, using messages is not the best way to implement certain functions.

This part focuses on practical data analysis in MQL5 with dataanalysis.mqh. We prepare a labeled dataset from bars, apply normalization, explore redundancy with PCA, and train a decision forest to classify future bar regimes. The article shows how to obtain out-of-bag estimates and permutation importance, helping you validate the model and understand which inputs matter most.

We decode ONNX files in pure MQL5 by implementing a Protocol Buffers reader from scratch. We generate a sample network in Python, verify it in Netron, and then parse the same binary to recover graph nodes, connections, weight tensors, and input/output shapes. The result is a MetaTrader 5 program that inspects a trained model's structure before inference, without any external libraries.

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.