Functional Time Series Analysis and Visualization Based on Records

In many phenomena, data are collected on a large scale and at 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 are very important in practice, can be challenging due to the complexity of the continuous functions. Here we introduce a type of record concept for functional data, and we propose some nonparametric tools based on the record concept for functional data observed over time (functional time series). 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 for 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: Daily wind speed curves at Yanbu, Saudi Arabia and annual mortality rates in France. Overall, we can identify the type of functional time series being studied based on the number of record curves observed. Supplementary materials for this article are available online.