Publications

A. Boudou and S. Viguier-Pla (2006)
On proximity between PCA in the frequency domain and usual PCA.
Statistics 40 447-464
ISSN: 0233-1888 DOI: 10.1080/02664760310001619350

Classification

62H12; 62H25; 62M15; 62P12

Keywords

applications, principal components analysis, random measure, spectral analysis, stationarity, time series

Abstract : The Principal Components Analysis (PCA) in the frequency domain of a stationary p-dimensional time series (Xn)(n in Z) leads to a summarizing time series written as a linear combination series Xn'=sum(m)Cm o X(n-m). Therefore, we observe that, when the coefficients Cm, m different from 0, are close to 0, this PCA is close to the usual PCA, that is the PCA in the temporal domain. When the coefficients tend to 0, the corresponding limit is said to satisfy a property noted P, of which we will study the consequences. Finally, we will examine, for any series, the proximity between the two PCA's.