Detecting Trends in Functional Time Series Data: Antarctic Climate Study

• Activity Number: 66
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Pamela Llop* and Ricardo Fraiman and Ana Justel and Regina Y. Liu
• Companies: IMAL(UNL-CONICET)/FIQ (UNL) and Universidad de la República and Universidad Autónoma de Madrid and Rutgers University
• Keywords: Functional Data ; Nonparametric tests ; Trends in functional data ; Global warming ; Antartica

Abstract

The Spanish Antarctic Station Juan Carlos I has been registering surface air temperatures with the frequency of one reading per ten minutes since the austral summer 1987-1988. Although this data set contains valuable information about the climate patterns in and around Antarctica, it has not been utilized in any existing climate studies thus far because of the concern of its substantial missing data caused by the difficulty in collecting data in the extreme winter weather conditions there. Such data sets do not fit the standard setting covered by the existing times series techniques. However, by treating the temperature readings for each summer as a function, the temperature data can be viewed as a time series of functional data. In this work, we introduce new notions of increasing trends for general time series of functional data based on the so-called record functions, and also develop useful nonparametric tests for such trends. Following our analysis, the data collected from Juan Carlos I Station exhibit an increasing trend in the Antarctic temperature.