Testing the structural stability of temporally dependent functional observations and application to climate projections

By Xianyang Zhang, Xiaofeng Shao, Katharine Hayhoe, D. Wuebbles. 2011

66 citations recorded by the source corpus.

Abstract: We develop a self-normalization (SN) based test to test the structural stability of temporally dependent functional observations. Testing for a change point in the mean of functional data has been studied in Berkes, Gabrys, Horvath and Kokoszka [4], but their test was developed under the independence assumption. In many applications, functional observations are expected to be dependent, especially when the data is collected over time. Building on the SN-based change point test proposed in Shao and Zhang [23] for a univariate time series, we extend the SNbased test to the functional setup by testing the constant mean of the finite dimensional eigenvectors after performing functional principal component analysis. Asymptotic theories are derived under both the null and local alternatives. Through theory and extensive simulations, our SN-based test statistic proposed in the functional setting is shown to inherit some useful properties in the univariate setup: the test is asymptotically distribution free and its power is monotonic. Furthermore, we extend the SN-based test to identify potential change points in the dependence structure of functional observations. The method is then applied to central England temperature series to detect the warming trend and to gridded temperature fields generated by global climate models to test for changes in spatial bias structure over time.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3c9f46cf8ec94c14a8884134bfece470e73b9d36

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Statistics and Probability

Citations in the corpus

Detection of change in the spatiotemporal mean function (2017, methodology): “Developing change point tools for functional data has been undertaken only in the last few years; Horváth et al. (2010), Berkes et al. (2009), Hörmann and Kokoszka (2010), Zhang et al. (2011) and Aston and Kirch (2012a,b).”
Testing relevant hypotheses in functional time series via self‐normalization (2018, background): “ch are based on FPCA. Another important research area in functional data analysis is change point detection and we refer to Berkes et al. (2009), Hormann and Kokoszka (2010), Aston and Kirch (2012), Zhang et al. (2011), Horvath et al. (2014), Bucchia and Wendler (2017) among others who investigate c”
Testing stationarity of functional time series (2014, background): “At present only CUSUM change point tests are available for functional time series, see Berkes et al. (2009), Horváth et al. (2010) and Zhang et al. (2011).”
A Plug‐in Bandwidth Selection Procedure for Long‐Run Covariance Estimation with Stationary Functional Time Series (2016, background): “…(2016), Aue et al. (2014), Aston and Kirch (2012a), Aston and Kirch (2012b), Horváth et al. (2012), Torgovitski (2016), Hörmann et al. (2015), Zhang (2016), & Zhang et al. (2011) for a sample of recent contributions that focus on inference, and dimension reduction with functional time-series data.”