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

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  • Reisen, Valdério Anselmo
  • Sgrancio, Adriano Marcio
  • Lévy-Leduc, Céline
  • Bondon, Pascal
  • Monte, Edson Zambon
  • Aranda Cotta, Higor Henrique
  • Ziegelmann, Flávio Augusto

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.

Suggested Citation

  • Reisen, Valdério Anselmo & Sgrancio, Adriano Marcio & Lévy-Leduc, Céline & Bondon, Pascal & Monte, Edson Zambon & Aranda Cotta, Higor Henrique & Ziegelmann, Flávio Augusto, 2019. "Robust factor modelling for high-dimensional time series: An application to air pollution data," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 842-852.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:842-852
    DOI: 10.1016/j.amc.2018.09.062
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    References listed on IDEAS

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    1. Ma, Yanyuan & Genton, Marc G., 2001. "Highly Robust Estimation of Dispersion Matrices," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 11-36, July.
    2. Clifford Lam & Qiwei Yao & Neil Bathia, 2011. "Estimation of latent factors for high-dimensional time series," Biometrika, Biometrika Trust, vol. 98(4), pages 901-918.
    3. Lam, Clifford & Yao, Qiwei & Bathia, Neil, 2011. "Estimation of latent factors for high-dimensional time series," LSE Research Online Documents on Economics 31549, London School of Economics and Political Science, LSE Library.
    4. Lordan, Oriol & Sallan, Jose M. & Escorihuela, Nuria & Gonzalez-Prieto, David, 2016. "Robustness of airline route networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 18-26.
    5. V. A. Reisen & C. Lévy-Leduc & M. Bourguignon & H. Boistard, 2017. "Robust Dickey–Fuller tests based on ranks for time series with additive outliers," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 115-131, January.
    6. Céline Lévy‐Leduc & Hélène Boistard & Eric Moulines & Murad S. Taqqu & Valderio A. Reisen, 2011. "Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 135-156, March.
    7. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    8. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
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