Constrained Recurrent Cubic Fractal Framework and Forecasting Based on Decision Tree Regression

Abstract

In this paper, we propose a Constrained Recurrent Cubic Fractal Model that integrates the Recurrent Iterated Function System with a constrained piecewise linear function to model complex datasets and establish its convergence analysis effectively. The proposed model employs rational cubic and quadratic  forms to ensure precise interpolation. To validate its effectiveness, we apply the model to real-world datasets, including stock data analyzed using decision tree regression. The integration of decision tree regression further enhances predictive performance, enabling accurate interpolation of existing data points and reliable forecasting of future values. Numerical experiments confirm that the model produces smooth and accurate interpolations, preserves underlying trends, and delivers consistent predictions across diverse datasets.
This study represents a significant advancement in recurrent fractal-based modeling methodologies for data analysis and forecasting.