Articles on data analysis and statistics in MQL5

The article is devoted to the practical application of the fuzzy logic concept for financial markets analysis. We propose the example of the indicator generating signals based on two fuzzy rules based on Envelopes indicator. The developed indicator uses several indicator buffers: 7 buffers for calculations, 5 buffers for the charts display and 2 color buffers.

The article compares the time and results of Expert Advisors' optimization using genetic algorithms and those obtained by simple search.

This article considers using the Rattle package for automatic search of patterns for predicting long and short positions of currency pairs on Forex. This article can be useful both for novice and experienced traders.

The article provides a critical examination of regular divergence and efficiency of various indicators. In addition, it contains filtering options for an increased analysis accuracy and features description of non-standard solutions. As a result, we will create a new tool for solving the technical task.

In the previous articles, we started creating a large cross-platform library simplifying the development of programs for MetaTrader 5 and MetaTrader 4 platforms. We already have collections of historical orders and deals, market orders and positions, as well as the class for convenient selection and sorting of orders. In this part, we will continue the development of the base object and teach the Engine Library to track trading events on the account.

In the article, we will consider a sample multi-symbol multi-period indicator using the timeseries classes of the DoEasy library displaying the chart of a selected currency pair on a selected timeframe as candles in a subwindow. I am going to modify the library classes a bit and create a separate file for storing enumerations for program inputs and selecting a compilation language.

In the article, we continue to develop the MQL application for working with optimization results. This time, we will show how to form the table of the best results after optimizing the parameters by specifying another criterion via the graphical interface.

In this article, we will apply the probability theory and mathematical statistics methods to creating and testing trading strategies. We will also look for optimal trading risk using the differences between the price and the random walk. It is proved that if prices behave like a zero-drift random walk (with no directional trend), then profitable trading is impossible.

Genetic (evolutionary) algorithms are used for optimization purposes. An example of such purpose can be neuronet learning, i.e., selection of such weight values that allow reaching the minimum error. At this, the genetic algorithm is based on the random search method.

This article seeks to upgrade the indicator created earlier on and briefly deals with a method for estimating forecast confidence intervals using bootstrapping and quantiles. As a result, we will get the forecast indicator and scripts to be used for estimation of the forecast accuracy.

The article gives formulas and the calculation order for data shown in the Tester report.

The MetaTrader 5 platform features functionality for saving trading reports, as well as Expert Advisor testing and optimization reports. Trading and testing reports can be saved in two formats: XLSX and HTML, while the optimization report can be saved in XML. In this article we consider the HTML testing report, the XML optimization report and the HTML trading history report.

After we send a trading order to the server, we need to check the error codes or the absence of errors. In this article, we will consider handling errors returned by the trade server and prepare for creating pending trading requests.

In this article, we will consider the class of displaying text messages. Currently, we have a sufficient number of different text messages. It is time to re-arrange the methods of their storage, display and translation of Russian or English messages to other languages. Besides, it would be good to introduce convenient ways of adding new languages to the library and quickly switching between them.

After the upgrade of the MATLAB package in 2015, it is necessary to consider a modern way of creating DLL libraries. The article uses a sample predictive indicator to illustrate the peculiarities of linking MetaTrader 5 and MATLAB using modern 64-bit versions of the platforms, which are utilized nowadays. With the entire sequence of connecting MATLAB considered, MQL5 developers will be able to create applications with advanced computational capabilities much faster, avoiding «pitfalls».

It is impossible to get a truly stable algorithm if we use optimization based on historical data to select parameters. A stable algorithm should be aware of what parameters are needed when working on any trading instrument at any time. It should not forecast or guess, it should know for sure.

This is a continuation of the idea of processing and analysis of optimization results. This time, our purpose is to select the 100 best optimization results and display them in a GUI table. The user will be able to select a row in the optimization results table and receive a multi-symbol balance and drawdown graph on separate charts.

There is no trouble finding the Holy Grail of testing, it is however much more difficult to get rid of it. This article addresses the selection of the Expert Advisor operating parameters with automated group processing of optimisation and testing results upon maximum utilisation of the Terminal performance capabilities and minimum end user load.

The scope of use of fractional differentiation is wide enough. For example, a differentiated series is usually input into machine learning algorithms. The problem is that it is necessary to display new data in accordance with the available history, which the machine learning model can recognize. In this article we will consider an original approach to time series differentiation. The article additionally contains an example of a self optimizing trading system based on a received differentiated series.

We continue the development of the library functionality featuring trading using pending requests. We have already implemented sending conditional trading requests for opening positions and placing pending orders. In the current article, we will implement conditional position closure – full, partial and closing by an opposite position.

The article deals with the creation of a program allowing to estimate the kernel density of the unknown probability density function. Kernel Density Estimation method has been chosen for executing the task. The article contains source codes of the method software implementation, examples of its use and illustrations.

The article demonstrates the capabilities and potential of a well-known mathematical method coupled with visual thinking and an "out of the box" market outlook. On the one hand, it serves to attract the attention of a wide audience as it can get the creative minds to reconsider the trading paradigm as such. And on the other, it can give rise to alternative developments and program code implementations regarding a wide range of tools for analysis and forecasting.

The article is intended to get its readers acquainted with the Box-Cox transformation. The issues concerning its usage are addressed and some examples are given allowing to evaluate the transformation efficiency with random sequences and real quotes.

The article deals with the approaches enabling accurate simulation of walk forward optimization using the built-in tester and auxiliary libraries implemented in MQL.

Different situations happen in trader’s life. Often, the history of successful trades allows us to restore a strategy, while looking at a loss history we try to develop and improve it. In both cases, we compare trades with known indicators. This article suggests methods of batch comparison of trades with a number of indicators.

In this article, we will continue the development of trading requests, implement placing pending orders and eliminate detected shortcomings of the trading class operation.

The article deals with the development of the timeseries collection of specified timeframes for all symbols used in the program. We are going to develop the timeseries collection, the methods of setting collection's timeseries parameters and the initial filling of developed timeseries with historical data.

In this article, we are going to finish the development of the base object of all library objects, so that any library object based on it is able to interact with a user. For example, users will be able to set the maximum acceptable size of a spread for opening a position and a price level, upon reaching which an event from a symbol object is sent to the program with the spread or price level-based signal.

The technical analysis widely implements the indicators showing the basic quotes "more clearly" and allowing traders to perform analysis and forecast market prices movement. It's quite obvious that there is no sense in using the indicators, let alone applying them in creation of trading systems, unless we can solve the issues concerning initial quotes transformation and the obtained result credibility. In this article we show that there are serious reasons for such a conclusion.

Studies related to search for the fractal behavior of financial data suggest that behind the seemingly chaotic behavior of economic time series there are hidden stable mechanisms of participants' collective behavior. These mechanisms can lead to the emergence of price dynamics on the exchange, which can define and describe specific properties of price series. When applied to trading, one could benefit from the indicators which can efficiently and reliably estimate the fractal parameters in the scale and time frame, which are relevant in practice.

In previous articles, we used stochastic gradient descent to train a neural network using the same learning rate for all neurons within the network. In this article, I propose to look towards adaptive learning methods which enable changing of the learning rate for each neuron. We will also consider the pros and cons of this approach.

In this article, we will have a look at the handler of invalid trading order parameters and improve the trading event class. Now all trading events (both single ones and the ones occurred simultaneously within one tick) will be defined in programs correctly.

This is the next article within the series, in which I show how I created a convenient library for manual application of chart graphics by utilizing keyboard shortcuts. The tools used include straight lines and their combinations. In this part, we will view how the drawing tools are applied using the functions described in the first part. The library can be connected to any Expert Advisor or indicator which will greatly simplify the charting tasks. This solution DOES NOT use external dlls, while all the commands are implemented using built-in MQL tools.

I continue filling the algorithm with the minimum necessary functionality and testing the results. The profitability is quite low but the articles demonstrate the model of the fully automated profitable trading on completely different instruments traded on fundamentally different markets.

We continue studying the world of neural networks. In this article, we will consider another type of neural networks, recurrent networks. This type is proposed for use with time series, which are represented in the MetaTrader 5 trading platform by price charts.

The article provides an overview of the terminal's capabilities for creating and working with custom symbols, offers options for simulating a trading history using custom symbols, trend and various chart patterns.

Trading is always about making decisions in the face of uncertainty. This means that the results of the decisions are not quite obvious at the time these decisions are made. This entails the importance of theoretical approaches to the construction of mathematical models allowing us to describe such cases in meaningful manner.

In this article we will continue dealing with the OLAP technology applied to trading. We will expand the functionality presented in the first two articles. This time we will consider the operational analysis of quotes. We will put forward and test the hypotheses on trading strategies based on aggregated historical data. The article presents Expert Advisors for studying bar patterns and adaptive trading.