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Title: Unit-root test for functional data based on records Authors:  Israel Martinez Hernandez - KAUST (Saudi Arabia) [presenting]
Marc Genton - KAUST (Saudi Arabia)
Abstract: A unit-root test for functional time series is proposed which based on records, where a record is a temporary maximum or minimum in the sequence of curves. The problem of unit roots in univariate time series has been deeply studied because of its importance in econometrics. However, economic and financial data can often be considered as a collection of curves over time. We extend the concept of records to functional data by using depth notions for curves, and we propose a new unit root test based on the ranks of the curves. We study the growth rate of the number of records over time and derive the asymptotic distribution of the test statistic. We present a Monte Carlo study to evaluate the performance of the proposed test and compare our test with the existing ones in the literature. We apply our method to a dataset of annual mortality rates in France.