Detecting trends in time series of functional data: A study of Antarctic climate change

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

Sequential block bootstrap in a Hilbert space with application to change point analysis

“…The method of functional principal components was used by Kokoszka et al () in testing for independence in the functional linear model and by Benko, Härdle, & Kneip () in two sample tests for ‐valued random variables, a method that was extended to change point analysis by Berkes et al (). Another approach is due to Fraiman et al () who used record functions to detect trends in functional data. In contrast to all former approaches, our method takes the fully functional observation into account.…”

Data‐driven dimension reduction in functional principal component analysis identifying the change‐point in functional data

“…Over the last few decades Functional Data Analysis (FDA) has become a topic of great interest in statistics, with applications to, for instance global warming and climate change [9], financial market data analysis [14], medicine [15], or engineering systems safety monitoring [7]. In many applications it is important to analyze a sequence of functional data that collected over time.…”

Nonparametric trend estimation in functional time series with application to annual mortality rates

“…This nonstationarity may be caused by structural breaks, functional random walk components, or deterministic trend components. Deterministic trends, or functional trends, can be observed in different phenomena where functional data approaches have been used, for example, growth curves (Ramsay and Silverman, 2005), annual mortality rates (Hyndman and Ullah, 2007), gene networks (Telesca et al, 2009), climate change (Fraiman et al, 2014), electricity power systems (Horváth and Rice, 2015), and electroencephalography (EEG) data (Hasenstab et al, 2017). The detection and estimation of the functional trend are crucial in data analysis, modeling, and forecasting.…”

“…A few attempts can be found in the literature on the study of functional trends. In Fraiman et al (2014), a functional trend was defined by using the concept of records, where a record means the occurrence of new extreme observations, but nothing was mentioned about the estimation. In Kokoszka and Young (2017), a hypothesis test of trend stationarity of functional time series was proposed.…”