Вычисление статистического спрэда методом Ньютона-Рафсона

Abstract

The statistical spread, defined as the difference between asset returns or prices, is a vital metric in financial analysis, particularly for pair trading and risk assessment. Traditional autoregressive models, such as AR(1) defined by 𝑆𝑡 = 𝑐 + 𝜙𝑆𝑡−1 + 𝜖𝑡, model spread dynamics using past values, with parameters estimated via the Newton-Raphson method for rapid convergence. However, these models often falter with nonlinear financial time series like Forex data. This study develops a program integrating AR models (AR(1), AR(2), ARX) with neural networks to enhance forecasting accuracy. Using Forex data accessed via APIs, the program collects and processes data, implements autoregressive models, applies the Newton-Raphson method for parameter estimation, and employs neural networks for predictions. The approach evaluates exogenous factors' impact, aiming for a hybrid model that outperforms standalone methods. Results suggest improved spread forecasting, valuable for financial analytics