Varying coefficient models are among the most important tools for discovering the dynamic patterns when a fixed pattern does not fit adequately well on the data, due to existing diverse temporal or local patterns. These models are natural extensions of classical parametric models that have achieved great popularity in data analysis with good interpretability. The high flexibility and interpretability of these models have led to use in many real applications. In this paper, after presenting a brief review of varying coefficient models, we use the parameter estimation method using the kernel function and cubic
spline then confidence band and hypothesis testing are investigated. Finally, using the real data of Iran’s inflation rate from 1989 to 2017, we show the application and capabilities of the varying coefficient model in interpreting the results. The main challenge in this application is that the panel or longitudinal models or even time series models with heterogeneous variances such as ARCH and GARCH models and their derived models did not fit adequately well on this dataset which justifies the use of varying coefficient models.