Dynamic functional principal components

By Siegfried Hormann, Łukasz Kidziński, Marc Hallin. 2012

215 citations recorded by the source corpus.

We address the problem of dimension reduction for time series of functional data (Xt:t∈Z) . Such functional time series frequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then each Xt represents one intraday curve. We argue that functional principal component analysis, though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time series setting. Functional principal component analysis indeed is a static procedure which ignores the essential information that is provided by the serial dependence structure of the functional data under study. Therefore, inspired by Brillinger's theory of dynamic principal components, we propose a dynamic version of functional principal component analysis which is based on a frequency domain approach. By means of a simulation study and an empirical illustration, we show the considerable improvement that the dynamic approach entails when compared with the usual static procedure.

Subfields: Analytical Chemistry, Applied Mathematics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/bd4f8e94fd4501a96c0d4c6e60b1c6d0ec6e7d1c

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In Analytical Chemistry

In Applied Mathematics

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Citations in the corpus

White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, background): “Finally, we point out that spectral analysis of stationary functional time series has been recently advanced by Panaretos and Tavakoli (2013a,b) and Hörmann et al. (2015).”
Generalized Dynamic Principal Components (2016, methodology): “The BDPCk components were computed using the R code developed for H örmann, Kidzí nski and Hallin (2014) that was kindly provided by the authors.”
Testing for stationarity of functional time series in the frequency domain (2017, methodology): “One should mention Panaretos & Tavakoli (2013), who provided results concerning the Fourier analysis of time series in function spaces, and Hörmann et al. (2015), who addressed the problem of dimension reduction for functional time series using dynamic principal components.”
Prediction of functional ARMA processes with an application to traffic data (2016, background): “In H¨ormann et al. [11] and Panaretros and Tavakoli [12] an optimal dimension reduction for dependent data is introduced.”
Locally Stationary Functional Time Series (2016, methodology): “In the case of stationary dependent functional data, the shape and smoothness properties of the random curves are completely encoded by the spectral density operator, which has been shown to allow for an optimal lower dimension representation via dynamic FPCA (see e.g., Panaretos and Tavakoli, 2013a”
Principal component analysis: a review and recent developments (2016, background): “A ‘dynamic’ version of functional PCA is proposed in [24], which is relevant when there are correlations between the observed curves, as well as the obvious correlation within the curves.”
Forecasting of density functions with an application to cross-sectional and intraday returns (2019, methodology): “Alternatively, a univariate ARIMA method or a multivariate time series forecasting method (Aue, Norinho, & Hörmann, 2015) can be used.”