Articles on data analysis and statistics in MQL5

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Articles on mathematical models and laws of probability are interesting for many traders. Mathematics is the basis of technical indicators, and statistics is required to analyze trading results and develop strategies.

Read about the fuzzy logic, digital filters, market profile, Kohonen maps, neural gas and many other tools that can be used for trading.

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Data Science and ML (Part 42): Forex Time series Forecasting using ARIMA in Python, Everything you need to Know

Data Science and ML (Part 42): Forex Time series Forecasting using ARIMA in Python, Everything you need to Know

ARIMA, short for Auto Regressive Integrated Moving Average, is a powerful traditional time series forecasting model. With the ability to detect spikes and fluctuations in a time series data, this model can make accurate predictions on the next values. In this article, we are going to understand what is it, how it operates, what you can do with it when it comes to predicting the next prices in the market with high accuracy and much more.
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Timeseries in DoEasy library (part 57): Indicator buffer data object

Timeseries in DoEasy library (part 57): Indicator buffer data object

In the article, develop an object which will contain all data of one buffer for one indicator. Such objects will be necessary for storing serial data of indicator buffers. With their help, it will be possible to sort and compare buffer data of any indicators, as well as other similar data with each other.
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Machine Learning Blueprint (Part 4): The Hidden Flaw in Your Financial ML Pipeline — Label Concurrency

Machine Learning Blueprint (Part 4): The Hidden Flaw in Your Financial ML Pipeline — Label Concurrency

Discover how to fix a critical flaw in financial machine learning that causes overfit models and poor live performance—label concurrency. When using the triple-barrier method, your training labels overlap in time, violating the core IID assumption of most ML algorithms. This article provides a hands-on solution through sample weighting. You will learn how to quantify temporal overlap between trading signals, calculate sample weights that reflect each observation's unique information, and implement these weights in scikit-learn to build more robust classifiers. Learning these essential techniques will make your trading models more robust, reliable and profitable.
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Analyzing all price movement options on the IBM quantum computer

Analyzing all price movement options on the IBM quantum computer

We will use a quantum computer from IBM to discover all price movement options. Sounds like science fiction? Welcome to the world of quantum computing for trading!
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MQL5 Wizard Techniques you should know (Part 78): Gator and AD Oscillator Strategies for Market Resilience

MQL5 Wizard Techniques you should know (Part 78): Gator and AD Oscillator Strategies for Market Resilience

The article presents the second half of a structured approach to trading with the Gator Oscillator and Accumulation/Distribution. By introducing five new patterns, the author shows how to filter false moves, detect early reversals, and align signals across timeframes. With clear coding examples and performance tests, the material bridges theory and practice for MQL5 developers.
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News Trading Made Easy (Part 6): Performing Trades (III)

News Trading Made Easy (Part 6): Performing Trades (III)

In this article news filtration for individual news events based on their IDs will be implemented. In addition, previous SQL queries will be improved to provide additional information or reduce the query's runtime. Furthermore, the code built in the previous articles will be made functional.
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Self Optimizing Expert Advisor With MQL5 And Python (Part V): Deep Markov Models

Self Optimizing Expert Advisor With MQL5 And Python (Part V): Deep Markov Models

In this discussion, we will apply a simple Markov Chain on an RSI Indicator, to observe how price behaves after the indicator passes through key levels. We concluded that the strongest buy and sell signals on the NZDJPY pair are generated when the RSI is in the 11-20 range and 71-80 range, respectively. We will demonstrate how you can manipulate your data, to create optimal trading strategies that are learned directly from the data you have. Furthermore, we will demonstrate how to train a deep neural network to learn to use the transition matrix optimally.
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MQL5 Wizard Techniques you should know (Part 08): Perceptrons

MQL5 Wizard Techniques you should know (Part 08): Perceptrons

Perceptrons, single hidden layer networks, can be a good segue for anyone familiar with basic automated trading and is looking to dip into neural networks. We take a step by step look at how this could be realized in a signal class assembly that is part of the MQL5 Wizard classes for expert advisors.
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Finding custom currency pair patterns in Python using MetaTrader 5

Finding custom currency pair patterns in Python using MetaTrader 5

Are there any repeating patterns and regularities in the Forex market? I decided to create my own pattern analysis system using Python and MetaTrader 5. A kind of symbiosis of math and programming for conquering Forex.
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William Gann methods (Part III): Does Astrology Work?

William Gann methods (Part III): Does Astrology Work?

Do the positions of planets and stars affect financial markets? Let's arm ourselves with statistics and big data, and embark on an exciting journey into the world where stars and stock charts intersect.
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Creating 3D bars based on time, price and volume

Creating 3D bars based on time, price and volume

The article dwells on multivariate 3D price charts and their creation. We will also consider how 3D bars predict price reversals, and how Python and MetaTrader 5 allow us to plot these volume bars in real time.
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Population optimization algorithms: Saplings Sowing and Growing up (SSG)

Population optimization algorithms: Saplings Sowing and Growing up (SSG)

Saplings Sowing and Growing up (SSG) algorithm is inspired by one of the most resilient organisms on the planet demonstrating outstanding capability for survival in a wide variety of conditions.
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Feature Engineering With Python And MQL5 (Part I): Forecasting Moving Averages For Long-Range AI Models

Feature Engineering With Python And MQL5 (Part I): Forecasting Moving Averages For Long-Range AI Models

The moving averages are by far the best indicators for our AI models to predict. However, we can improve our accuracy even further by carefully transforming our data. This article will demonstrate, how you can build AI Models capable of forecasting further into the future than you may currently be practicing without significant drops to your accuracy levels. It is truly remarkable, how useful the moving averages are.
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Category Theory in MQL5 (Part 2)

Category Theory in MQL5 (Part 2)

Category Theory is a diverse and expanding branch of Mathematics which as of yet is relatively uncovered in the MQL5 community. These series of articles look to introduce and examine some of its concepts with the overall goal of establishing an open library that attracts comments and discussion while hopefully furthering the use of this remarkable field in Traders' strategy development.
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MQL5 Wizard Techniques you should know (Part 25): Multi-Timeframe Testing and Trading

MQL5 Wizard Techniques you should know (Part 25): Multi-Timeframe Testing and Trading

Strategies that are based on multiple time frames cannot be tested in wizard assembled Expert Advisors by default because of the MQL5 code architecture used in the assembly classes. We explore a possible work around this limitation for strategies that look to use multiple time frames in a case study with the quadratic moving average.
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Portfolio Risk Model using Kelly Criterion and Monte Carlo Simulation

Portfolio Risk Model using Kelly Criterion and Monte Carlo Simulation

For decades, traders have been using the Kelly Criterion formula to determine the optimal proportion of capital to allocate to an investment or bet to maximize long-term growth while minimizing the risk of ruin. However, blindly following Kelly Criterion using the result of a single backtest is often dangerous for individual traders, as in live trading, trading edge diminishes over time, and past performance is no predictor of future result. In this article, I will present a realistic approach to applying the Kelly Criterion for one or more EA's risk allocation in MetaTrader 5, incorporating Monte Carlo simulation results from Python.
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Developing a Replay System (Part 27): Expert Advisor project — C_Mouse class (I)

Developing a Replay System (Part 27): Expert Advisor project — C_Mouse class (I)

In this article we will implement the C_Mouse class. It provides the ability to program at the highest level. However, talking about high-level or low-level programming languages is not about including obscene words or jargon in the code. It's the other way around. When we talk about high-level or low-level programming, we mean how easy or difficult the code is for other programmers to understand.
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GIT: What is it?

GIT: What is it?

In this article, I will introduce a very important tool for developers. If you are not familiar with GIT, read this article to get an idea of what it is and how to use it with MQL5.
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MQL5 Wizard Techniques you should know (Part 19): Bayesian Inference

MQL5 Wizard Techniques you should know (Part 19): Bayesian Inference

Bayesian inference is the adoption of Bayes Theorem to update probability hypothesis as new information is made available. This intuitively leans to adaptation in time series analysis, and so we have a look at how we could use this in building custom classes not just for the signal but also money-management and trailing-stops.
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Brain Storm Optimization algorithm (Part II): Multimodality

Brain Storm Optimization algorithm (Part II): Multimodality

In the second part of the article, we will move on to the practical implementation of the BSO algorithm, conduct tests on test functions and compare the efficiency of BSO with other optimization methods.
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Price Action Analysis Toolkit Development (Part 29): Boom and Crash Interceptor EA

Price Action Analysis Toolkit Development (Part 29): Boom and Crash Interceptor EA

Discover how the Boom & Crash Interceptor EA transforms your charts into a proactive alert system-spotting explosive moves with lightning-fast velocity scans, volatility surge checks, trend confirmation, and pivot-zone filters. With crisp green “Boom” and red “Crash” arrows guiding your every decision, this tool cuts through the noise and lets you capitalize on market spikes like never before. Dive in to see how it works and why it can become your next essential edge.
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Neural networks made easy (Part 34): Fully Parameterized Quantile Function

Neural networks made easy (Part 34): Fully Parameterized Quantile Function

We continue studying distributed Q-learning algorithms. In previous articles, we have considered distributed and quantile Q-learning algorithms. In the first algorithm, we trained the probabilities of given ranges of values. In the second algorithm, we trained ranges with a given probability. In both of them, we used a priori knowledge of one distribution and trained another one. In this article, we will consider an algorithm which allows the model to train for both distributions.
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Population optimization algorithms: Nelder–Mead, or simplex search (NM) method

Population optimization algorithms: Nelder–Mead, or simplex search (NM) method

The article presents a complete exploration of the Nelder-Mead method, explaining how the simplex (function parameter space) is modified and rearranged at each iteration to achieve an optimal solution, and describes how the method can be improved.
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Using association rules in Forex data analysis

Using association rules in Forex data analysis

How to apply predictive rules of supermarket retail analytics to the real Forex market? How are purchases of cookies, milk and bread related to stock exchange transactions? The article discusses an innovative approach to algorithmic trading based on the use of association rules.
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Price Action Analysis Toolkit Development (Part 31): Python Candlestick Recognition Engine (I) — Manual Detection

Price Action Analysis Toolkit Development (Part 31): Python Candlestick Recognition Engine (I) — Manual Detection

Candlestick patterns are fundamental to price-action trading, offering valuable insights into potential market reversals or continuations. Envision a reliable tool that continuously monitors each new price bar, identifies key formations such as engulfing patterns, hammers, dojis, and stars, and promptly notifies you when a significant trading setup is detected. This is precisely the functionality we have developed. Whether you are new to trading or an experienced professional, this system provides real-time alerts for candlestick patterns, enabling you to focus on executing trades with greater confidence and efficiency. Continue reading to learn how it operates and how it can enhance your trading strategy.
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Population optimization algorithms: Bat algorithm (BA)

Population optimization algorithms: Bat algorithm (BA)

In this article, I will consider the Bat Algorithm (BA), which shows good convergence on smooth functions.
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Data Science and Machine Learning (Part 17): Money in the Trees? The Art and Science of Random Forests in Forex Trading

Data Science and Machine Learning (Part 17): Money in the Trees? The Art and Science of Random Forests in Forex Trading

Discover the secrets of algorithmic alchemy as we guide you through the blend of artistry and precision in decoding financial landscapes. Unearth how Random Forests transform data into predictive prowess, offering a unique perspective on navigating the complex terrain of stock markets. Join us on this journey into the heart of financial wizardry, where we demystify the role of Random Forests in shaping market destiny and unlocking the doors to lucrative opportunities
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MQL5 Trading Toolkit (Part 8): How to Implement and Use the History Manager EX5 Library in Your Codebase

MQL5 Trading Toolkit (Part 8): How to Implement and Use the History Manager EX5 Library in Your Codebase

Discover how to effortlessly import and utilize the History Manager EX5 library in your MQL5 source code to process trade histories in your MetaTrader 5 account in this series' final article. With simple one-line function calls in MQL5, you can efficiently manage and analyze your trading data. Additionally, you will learn how to create different trade history analytics scripts and develop a price-based Expert Advisor as practical use-case examples. The example EA leverages price data and the History Manager EX5 library to make informed trading decisions, adjust trade volumes, and implement recovery strategies based on previously closed trades.
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Category Theory in MQL5 (Part 18): Naturality Square

Category Theory in MQL5 (Part 18): Naturality Square

This article continues our series into category theory by introducing natural transformations, a key pillar within the subject. We look at the seemingly complex definition, then delve into examples and applications with this series’ ‘bread and butter’; volatility forecasting.
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Trading Insights Through Volume: Moving Beyond OHLC Charts

Trading Insights Through Volume: Moving Beyond OHLC Charts

Algorithmic trading system that combines volume analysis with machine learning techniques, specifically LSTM neural networks. Unlike traditional trading approaches that primarily focus on price movements, this system emphasizes volume patterns and their derivatives to predict market movements. The methodology incorporates three main components: volume derivatives analysis (first and second derivatives), LSTM predictions for volume patterns, and traditional technical indicators.
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Developing a Replay System (Part 59): A New Future

Developing a Replay System (Part 59): A New Future

Having a proper understanding of different ideas allows us to do more with less effort. In this article, we'll look at why it's necessary to configure a template before the service can interact with the chart. Also, what if we improve the mouse pointer so we can do more things with it?
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Portfolio optimization in Forex: Synthesis of VaR and Markowitz theory

Portfolio optimization in Forex: Synthesis of VaR and Markowitz theory

How does portfolio trading work on Forex? How can Markowitz portfolio theory for portfolio proportion optimization and VaR model for portfolio risk optimization be synthesized? We create a code based on portfolio theory, where, on the one hand, we will get low risk, and on the other, acceptable long-term profitability.
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Quantum computing and trading: A fresh approach to price forecasts

Quantum computing and trading: A fresh approach to price forecasts

The article describes an innovative approach to forecasting price movements in financial markets using quantum computing. The main focus is on the application of the Quantum Phase Estimation (QPE) algorithm to find prototypes of price patterns allowing traders to significantly speed up the market data analysis.
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Robustness Testing on Expert Advisors

Robustness Testing on Expert Advisors

In strategy development, there are many intricate details to consider, many of which are not highlighted for beginner traders. As a result, many traders, myself included, have had to learn these lessons the hard way. This article is based on my observations of common pitfalls that most beginner traders encounter when developing strategies on MQL5. It will offer a range of tips, tricks, and examples to help identify the disqualification of an EA and test the robustness of our own EAs in an easy-to-implement way. The goal is to educate readers, helping them avoid future scams when purchasing EAs as well as preventing mistakes in their own strategy development.
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Price Action Analysis Toolkit Development (Part 50): Developing the RVGI, CCI and SMA Confluence Engine in MQL5

Price Action Analysis Toolkit Development (Part 50): Developing the RVGI, CCI and SMA Confluence Engine in MQL5

Many traders struggle to identify genuine reversals. This article presents an EA that combines RVGI, CCI (±100), and an SMA trend filter to produce a single clear reversal signal. The EA includes an on-chart panel, configurable alerts, and the full source file for immediate download and testing.
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Developing a Replay System (Part 32): Order System (I)

Developing a Replay System (Part 32): Order System (I)

Of all the things that we have developed so far, this system, as you will probably notice and eventually agree, is the most complex. Now we need to do something very simple: make our system simulate the operation of a trading server. This need to accurately implement the way the trading server operates seems like a no-brainer. At least in words. But we need to do this so that the everything is seamless and transparent for the user of the replay/simulation system.
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Developing a Replay System — Market simulation (Part 17): Ticks and more ticks (I)

Developing a Replay System — Market simulation (Part 17): Ticks and more ticks (I)

Here we will see how to implement something really interesting, but at the same time very difficult due to certain points that can be very confusing. The worst thing that can happen is that some traders who consider themselves professionals do not know anything about the importance of these concepts in the capital market. Well, although we focus here on programming, understanding some of the issues involved in market trading is paramount to what we are going to implement.
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A New Approach to Custom Criteria in Optimizations (Part 1): Examples of Activation Functions

A New Approach to Custom Criteria in Optimizations (Part 1): Examples of Activation Functions

The first of a series of articles looking at the mathematics of Custom Criteria with a specific focus on non-linear functions used in Neural Networks, MQL5 code for implementation and the use of targeted and correctional offsets.
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From Novice to Expert: Reporting EA — Setting up the work flow

From Novice to Expert: Reporting EA — Setting up the work flow

Brokerages often provide trading account reports at regular intervals, based on a predefined schedule. These firms, through their API technologies, have access to your account activity and trading history, allowing them to generate performance reports on your behalf. Similarly, the MetaTrader 5 terminal stores detailed records of your trading activity, which can be leveraged using MQL5 to create fully customized reports and define personalized delivery methods.
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Estimate future performance with confidence intervals

Estimate future performance with confidence intervals

In this article we delve into the application of boostrapping techniques as a means to estimate the future performance of an automated strategy.