Detecting trends in time series of functional data: A study of Antarctic climate change. Issue 4 (3rd November 2014) - Fraiman, Ricardo; Justel, Ana; Liu, Regina; Llop, Pamela
Abstract The Spanish Antarctic Station Juan Carlos I has been registering surface air temperatures with the frequency of one reading per 10 min 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. 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. The Canadian Journal of Statistics 42: 597–609; 2014 © 2014 Statistical Society of Canada