Articles
Uncertainty as a Model (Part 6): Multiple Regression and Diagnostics for MetaTrader 5
A practical introduction to multiple regression with deterministic factors for financial time series. Topics covered include the formulation and matrix form of ordinary least squares (OLS), residual diagnostics, EDA/CDA, R-squared and adjusted R-squared, the F-test, RESET, the Breusch–Pagan test
Uncertainty as a Model (Part 5): The Basics of Regression for MetaTrader 5
A practical introduction to time series regression models: regression on a constant and simple regression with deterministic, exogenous, and endogenous regressors. It describes the key steps in the diagnostic process, including residual analysis and hypothesis testing, that are necessary for making
Uncertainty as a Model (Part 4): Random Processes — The Dynamics of Uncertainty for MetaTrader 5
The article introduces the concepts and tools for working with random processes in trading: definitions, characteristics, autocorrelation functions, and a practical classification. The article covers white noise, random walks, Wiener and Poisson processes, as well as Markov chains and martingales
Uncertainty as a Model (Part 3): Mathematical Statistics — How to Extract Knowledge from Data for MetaTrader 5
This part of the series examines the mechanisms of the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) as the theoretical foundation for understanding market patterns. This section describes the tools of descriptive statistics and methods for finding point and interval estimates of
Uncertainty as a Model (Part 2): Dependence Among Random Variables — From Correlation to Copulas for MetaTrader 5
The second part of the series examines the mathematical framework for multivariate random variables, which is necessary for analyzing the dependence and joint behavior of market assets. This section describes joint distribution functions, the concepts of marginal and conditional distributions, and
Uncertainty as a Model (Part 1): Random Variables — The Language of Uncertainty for MetaTrader 5
The article provides a systematic overview of the theory of random variables, which serves as the basis for analyzing and modeling uncertainty in financial markets. The article covers the definitions and properties of univariate random variables, cumulative distribution functions (CDFs) and
Probability theory and mathematical statistics with examples (part I): Fundamentals and elementary theory for MetaTrader 5
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
Applying the probability theory to trading gaps for MetaTrader 5
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
Applying the Monte Carlo method for optimizing trading strategies for MetaTrader 5
Before launching a robot on a trading account, we usually test and optimize it on quotes history. However, a reasonable question arises: how can past results help us in the future? The article describes applying the Monte Carlo method to construct custom criteria for trading strategy optimization
Risk Evaluation in the Sequence of Deals with One Asset. Continued for MetaTrader 5
The article develops the ideas proposed in the previous part and considers them further. It describes the problems of yield distributions, plotting and studying statistical regularities