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In many phenomena, data are collected on a large scale and of differentfrequencies. In this context, functional data analysis (FDA) has become animportant statistical methodology for analyzing and modeling such data. Theapproach of FDA is to assume that data are continuous functions and that eachcontinuous function is considered as a single observation. Thus, FDA deals withlarge-scale and complex data. However, visualization and exploratory dataanalysis, which is very important in practice, can be challenging due to thecomplexity of the continuous functions. Here we propose some nonparametrictools for functional data observed over time (functional time series). Forthat, we propose to use the concept of record. We study the properties of thetrajectory of the number of record curves under different scenarios. Also, wepropose a unit root test based on the number of records. The trajectory of thenumber of records over time and the unit root test can be used as visualizationand exploratory data analysis. We illustrate the advantages of our proposalthrough a Monte Carlo simulation study. We also illustrate our method on twodifferent datasets: Annual mortality rates in France and daily wind speedcurves at Yanbu, Saudi Arabia. Overall, we can identify the type of functionaltime series being studied based on the number of record curves observed.

Functional Time Series Analysis Based on Records