  Aggregation of large databases in a specific format is a frequently used
process to make the data easily manageable. Interval-valued data is one of the
data types that is generated by such an aggregation process. Using traditional
methods to analyze interval-valued data results in loss of information, and
thus, several interval-valued data models have been proposed to gather reliable
information from such data types. On the other hand, recent technological
developments have led to high dimensional and complex data in many application
areas, which may not be analyzed by traditional techniques. Functional data
analysis is one of the most commonly used techniques to analyze such complex
datasets. While the functional extensions of much traditional statistical
techniques are available, the functional form of the interval-valued data has
not been studied well. This paper introduces the functional forms of some
well-known regression models that take interval-valued data. The proposed
methods are based on the function-on-function regression model, where both the
response and predictor/s are functional. Through several Monte Carlo
simulations and empirical data analysis, the finite sample performance of the
proposed methods is evaluated and compared with the state-of-the-art.
