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Principal components analysis of nonstationary time series data

  • Joseph Ryan G. Lansangan
  • Erniel B. BarriosEmail author
Article

Abstract

The effect of nonstationarity in time series columns of input data in principal components analysis is examined. Nonstationarity are very common among economic indicators collected over time. They are subsequently summarized into fewer indices for purposes of monitoring. Due to the simultaneous drifting of the nonstationary time series usually caused by the trend, the first component averages all the variables without necessarily reducing dimensionality. Sparse principal components analysis can be used, but attainment of sparsity among the loadings (hence, dimension-reduction is achieved) is influenced by the choice of parameter(s) (λ 1,i ). Simulated data with more variables than the number of observations and with different patterns of cross-correlations and autocorrelations were used to illustrate the advantages of sparse principal components analysis over ordinary principal components analysis. Sparse component loadings for nonstationary time series data can be achieved provided that appropriate values of λ 1,j are used. We provide the range of values of λ 1,j that will ensure convergence of the sparse principal components algorithm and consequently achieve sparsity of component loadings.

Keywords

Principal components analysis Sparse principal components analysis Time series Nonstationarity Singular value decomposition 

References

  1. Arnold, S.F.: The Theory of Linear Models and Multivariate Analysis. New York, Wiley (1981) zbMATHGoogle Scholar
  2. Chipman, H., Gu, H.: Interpretable dimension reduction. J. Appl. Stat. 32(9), 969–987 (2005) zbMATHCrossRefMathSciNetGoogle Scholar
  3. Fernandez-Macho, F.: A dynamic factor model for economic time series. Kybernetika 33(6), 583–606 (1997) zbMATHMathSciNetGoogle Scholar
  4. Gervini, D., Rousson, V.: Criteria for evaluating dimension-reducing components for multivariate data. Am. Stat. 58(1), 72–76 (2004) CrossRefMathSciNetGoogle Scholar
  5. Heaton, C., Solo, V.: Identification of causal factor models of stationary time series. Econom. J. 7(2), 618–627 (2004) zbMATHCrossRefMathSciNetGoogle Scholar
  6. Jolliffe, I.T.: Principal Component Analysis, 2nd ed. Springer, New York (2002) zbMATHGoogle Scholar
  7. Jolliffe, I.T., Uddin, M.: The simplified component technique: an alternative to rotated principal components. J. Comput. Graph. Stat. 9, 689–710 (2000) CrossRefMathSciNetGoogle Scholar
  8. Magnus, J.R., Neudecker, H.: Matrix Differential Calculus with Applications in Statistics and Economics. New York, Wiley (1999) Google Scholar
  9. Rousson, V., Gasser, T.: Simple component analysis. Appl. Stat. 53(4), 539–555 (2004) zbMATHMathSciNetGoogle Scholar
  10. Vines, S.: Simple principal components. Appl. Stat. 49(4), 441–451 (2000) zbMATHMathSciNetGoogle Scholar
  11. Zou, H., Hastie, T., Tibshirani, R.: Sparse principal components analysis. J. Comput. Graph. Stat. 15(2), 265–286 (2006) CrossRefMathSciNetGoogle Scholar
  12. Zuur, A.F., Tuck, I.D., Bailey, N.: Dynamic factor analysis to estimate common trends in fisheries time series. Can. J. Fish Aquat. Sci. 60, 542–552 (2003) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Joseph Ryan G. Lansangan
    • 1
  • Erniel B. Barrios
    • 1
    Email author
  1. 1.School of StatisticsUniversity of the Philippines DilimanQuezon CityPhilippines

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