Robust factor modelling for high-dimensional time series: An application to air pollution data

Valdério Anselmo Reisen (1) , Adriano Marcio Sgrancio (1) , Céline Lévy-Leduc (2) , Edson Zambon Monte (1) , Higor Henrique Aranda Cotta (1) , Pascal Bondon (3) , Flávio Augusto Ziegelmann (4)

1 Federal University of Espírito Santo
2 MIA-Paris - Mathématiques et Informatique Appliquées
3 L2S - Laboratoire des signaux et systèmes
4 UFRGS - Universidade Federal do Rio Grande do Sul [Porto Alegre]

Abstract This paper considers the factor modelling for high-dimensional time series contaminated by additive outliers. We propose a robust variant of the estimation method given in Lam and Yao [10]. The estimator of the number of factors is obtained by an eigen analysis of a robust non-negative definite covariance matrix. Asymptotic properties of the robust eigenvalues are derived and we show that the resulting estimators have the same convergence rates as those found for the standard eigenvalues estimators. Simulations are carried out to analyse the finite sample size performance of the robust estimator of the number of factors under the scenarios of multivariate time series with and without additive outliers. As an application, the robust factor analysis is performed to reduce the dimensionality of the data and, therefore, to identify the pollution behaviour of the pollutant PM10.

Mots clés: Reduced rank; Air pollution; Eigenvalues; Robustness; Time series; Factor analysis

Domaines: Statistiques [stat]; Méthodologie [stat.ME]

Valdério Anselmo Reisen, Adriano Marcio Sgrancio, Céline Lévy-Leduc, Edson Zambon Monte, Higor Henrique Aranda Cotta, et al.. Robust factor modelling for high-dimensional time series: An application to air pollution data. Applied Mathematics and Computation, 2019, 346, pp.842-852. ⟨10.1016/j.amc.2018.09.062⟩. ⟨hal-02902032⟩