Detection of Change in the Spatiotemporal Mean Function

Abstract

The paper develops inferential methodology for detecting a change in the annual pattern of an environmental variable measured at fixed locations in a spatial region. Using a framework built on functional data analysis, we model observations as a collection of functionvalued time sequences available at many sites. Each sequence is modelled as an annual mean function, which may change, plus a sequence of error functions, which are spatially correlated.The tests statistics extend the cumulative sum paradigm to this more complex setting. Their asymptotic distributions are not parameter free because of the spatial dependence but can be effectively approximated by Monte Carlo simulations. The new methodology is applied to precipitation data. Its finite sample performance is assessed by a simulation study.

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

“…() and for spatially distributed functional data in Gromenko et al . (). Smooth deviations from stationarity of functional time series in the frequenay domain were studied in Aue and van Delft ().…”

“…In Zhang et al (2011), a structural break detection procedure for serially correlated functional time series data was proposed that is based on the self-normalization approach of Shao and Zhang (2010). Structual break detection in the context of functional linear models was considered in Aue et al (2014) and for spatially distributed functional data in Gromenko et al (2017). Smooth deviations from stationarity of functional time series in the frequenay domain were studied in Aue and van Delft (2017).…”

Time series analysis of COVID-19 infection curve: A change-point perspective

“…In recent years, change-point analysis has become an increasingly active research area in statistics and econometrics thanks to its applications across a wide range of fields, including bioinformatics ( Fan and Mackey, 2017 ), climate science ( Gromenko et al, 2017 ), economics ( Bai, 1994 , Bai, 1997 , Cho and Fryzlewicz, 2015 ), finance ( Fryzlewicz, 2014 ), medical science ( Chen and Gupta, 2011 ), and signal processing ( Chen and Gu, 2018 ); see Perron (2006) , Aue and Horváth (2013) and Truong et al (2020) for some recent reviews. However, most existing change-point literature operates under the piecewise stationarity assumption, where it is assumed that the time series of interest is (potentially) non-stationary but can be partitioned into piecewise stationary segments such that observations within each segment are stationary and share a common parameter of interest such as mean or variance.…”

Principal Components Analysis of Periodically Correlated Functional Time Series

“…Examples of FTS include annual temperature or smoothed precipitation curves, e.g. Gromenko et al , daily pollution level curves, e.g. Aue et al , various daily curves derived from high‐frequency asset price data, e.g.…”