Proposing an Innovative Model Based on the Sierpinski Triangle for Forecasting EUR/USD Direction Changes

Abstract

The Sierpinski triangle is a fractal that is commonly used due to some of its characteristics and features. The Forex financial market is among the places wherein this triangle's characteristics are effective in forecasting the prices and their direction changes for the selection of the proper trading strategy and risk reduction. This study presents a novel approach to the Sierpinski triangle and introduces an innovative model based on it to forecast the direction changes in currency pairs, particularly EUR/USD. The model proposed in this study is dependent on the number of data selected for forecasting. The number of data is, in fact, the area of the initial triangle and the forecasted value of the self-similar triangles formed in each stage. For the performance assessment of the proposed method within one year (03/01/2019 to 28/02/2020), daily EUR/USD closed price data was classified into three categories, namely the training (70%), testing (20%), and validation (10%). Three approaches were proposed that led to forecasting the mean direction accuracy and the best result of over 60 percent in the third approach and over 50 percent in the first and second approaches. Results reflect the satisfactory improvements in the third approach compared to the econometrics, time-series, and machine learning methods. Moreover, the optimal number of data for the model is selected such that the difference between the accuracy of the direction forecasting in the training category and testing category is above 0.6 and below 0.05.