When data do not follow a fixed linear pattern and have diverse patterns dynamically in time or space, models with variable coefficients are considered as the most important tool for discovering dynamic patterns in them. These models are a natural extension of classical parametric models that have gained great popularity in data analysis due to their good interpretability. The high flexibility and interpretability of these models have led to their wide application in real data.
In this article, while briefly reviewing models with variable coefficients, we will discuss the parameter estimation method using the kernel function and cubic spline and obtain confidence intervals and hypothesis tests for parameter functions. Finally, using real data on Iran's inflation rate from 1989 to 2017, we show the application and capabilities of the model with variable coefficients in interpreting the results. The main challenge is the lack of proper fit of the panel data model and models with non-constant variance of time leads, such as ARCH and GARCH models and their derivatives, to these data, which justifies the use of models with variable coefficients.