This paper develops a method to find fractal curves to fit real data. With a formulation for fractal functions through a type of affine systems of iterative functional equations, we apply the procedure of minimizing the sum of square residuals that is used in the classical linear regression. We develop formulas for approximation and exact fractal functions for various fractal levels and number of equations. This method gives estimates for the parameters of the equations and corresponding functions, namely the fractal coefficients (vertical scaling factors) and directional coefficients. As a consequence, it is possible to upper estimate the Hausdorff dimension of the fitted curve. We provide worked examples, including estimating a fractal curve for a time series real data set of exchange rates between USD and EUR currencies.

本文开发了一种寻找分形曲线以拟合真实数据的方法。通过一种通过迭代函数方程的仿射系统的分形函数公式，我们应用了经典线性回归中使用的最小化残差平方和的过程。我们为各种分形水平和方程数量开发了近似和精确分形函数的公式。该方法对方程和相应函数的参数进行估计，即分形系数（垂直比例因子）和方向系数。因此，可以对拟合曲线的 Hausdorff 维数进行较高估计。我们提供了工作示例，包括为美元和欧元货币之间汇率的时间序列真实数据集估计分形曲线。