Generalized Records for Functional Time Series with Application to Unit Root Tests
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A generalization of the definition of records to functional data is proposed. The definition is based on ranking curves using a notion of functional depth. This approach allows us to study the curves of the number of records over time. We focus on functional time series and apply ideas from univariate time series to demonstrate the asymptotic distribution describing the number of records. A unit root test is proposed as an application of functional record theory. Through a Monte Carlo study, different scenarios of functional processes are simulated to evaluate the performance of the unit root test. The generalized record definition is applied on two different datasets: Annual mortality rates in France and daily curves of wind speed at Yanbu, Saudi Arabia. The record curves are identified and the underlying functional process is studied based on the number of record curves observed.
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