Analysis the economic and financial phenomena and other requires to build the appropriate model, which represents the causal relations between factors. The operation building of the model depends on Imaging conditions and factors surrounding an in mathematical formula and the Researchers target to build that formula appropriately. Classical linear regression models are an important statistical tool, but used in a limited way, where is assumed that the relationship between the variables illustrations and response variables identifiable. To expand the representation of relationships between variables that represent the phenomenon under discussion we used Varying Coefficient Models (VCM) as it assumes the effects of variables illustrations be variable adoption of another explanatory variable. These structural avoided what is known as Curse of Dimensionality, which appears when we used nonparametric methods in estimation. We estimate the varying coefficients by using nonparametric methods which is the Local Polynomial Kernel (LPK) and Penalized Spline (PS), and by using simulation technique for comparison we found that the LPK method is the best.
