In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA is to assume that data are continuous functions and that each continuous function is considered as a single observation. Thus, FDA deals with large-scale and complex data. However, visualization and exploratory data analysis, which is very important in practice, can be challenging due to the complexity of the continuous functions. Here we propose some nonparametric tools for functional data observed over time (functional time series). For that, we propose to use the concept of record. We study the properties of the trajectory of the number of record curves under different scenarios. Also, we propose a unit root test based on the number of records. The trajectory of the number of records over time and the unit root test can be used as visualization and exploratory data analysis. We illustrate the advantages of our proposal through a Monte Carlo simulation study. We also illustrate our method on two different datasets: Annual mortality rates in France and daily wind speed curves at Yanbu, Saudi Arabia. Overall, we can identify the type of functional time series being studied based on the number of record curves observed.