Dynamic functional principal components

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 77, Issue 2, 2015, Pages 319-348

  Hörmann, Siegfried ^a   Kidzi, Lukasz ^a   Hallin, Marc ^a,b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Dimension reduction; Frequency domain analysis; Functional data analysis; Functional spectral analysis; Functional time series; Karhunen Lo ve expansion; Principal components

Indexed keywords

EID: 84922159371     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/rssb.12076     Document Type: Article

References (36)

1. Aston, J. A. D. and Kirch, C. (2011) Estimation of the distribution of change-points with application to fMRI data. Technical Report. Centre for Research in Statistical Methodology, University of Warwick, Coventry.
2. Aue, A., Dubart Norinho, D. and Hörmann, S. (2014) On the prediction of functional time series. J. Am. Statist. Ass., to be published.
3. Benko, M., Härdle, W. and Kneip, A. (2009) Common functional principal components. Ann Statist., 37, 1-34.
4. Berkes, I., Gabrys, R., Horváth, L. and Kokoszka, P. (2009) Detecting changes in the mean of functional observations. J. R. Statist. Soc. B, 71, 927-946.
5. Besse, P. and Ramsay, J. O. (1986) Principal components analysis of sampled functions. Psychometrika, 51, 285-311.
6. Bosq, D. (2000) Linear Processes in Function Spaces. New York: Springer.
7. Brillinger, D. R. (1981) Time Series: Data Analysis and Theory. San Francisco: Holden-Day.
8. Brockwell, P. J. and Davis, R. A. (1981) Time Series: Theory and Methods. New York: Springer.
9. Cardot, H., Ferraty, F. and Sarda, P. (1999) Functional linear model. Statist. Probab. Lett., 45, 11-22.
10. Dauxois, J., Pousse, A. and Romain, Y. (1982) Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference. J. Multiv. Anal., 12, 136-154.
11. Ferraty, F. and Vieu, P. (2006) Nonparametric Functional Data Analysis. New York: Springer.
12. Gervini, D. (2007) Robust functional estimation using the median and spherical principal components. Biometrika, 95, 587-600.
13. Gohberg, I., Goldberg, S. and Kaashoek, M. A. (2003) Basic Classes of Linear Operators. Boston: Birkhäuser.
14. Gokulakrishnan, P., Lawrence, P. D., McLellan, P. J. and Grandmaison, E. W. (2006) A functional-PCA approach for analyzing and reducing complex chemical mechanisms. Comput. Chem. Engng, 30, 1093-1101.
15. Hall, P. and Hosseini-Nasab, M. (2006) On properties of functional principal components analysis. J. R. Statist. Soc. B, 68, 109-126.
16. Hall, P., Müller, H.-G. and Wang, J.-L. (2006) Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist., 34, 1493-1517.
17. Hörmann, S. and Kokoszka, P. (2010) Weakly dependent functional data. Ann. Statist., 38, 1845-1884.
18. Hörmann, S. and Kokoszka, P. (2012) Functional time series. In Handbook of Statistics: Time Series Analysis-Methods and Applications, pp. 157-186.
19. Hyndman, R. J. and Ullah, M. S. (2007) Robust forecasting of mortality and fertility rates: a functional data approach. Computnl Statist. Data Anal., 51, 4942-4956.
20. James, G. M., Hastie T. J. and Sugar, C. A. (2000) Principal component models for sparse functional data. Biometrika., 87, 587-602.
21. Jolliffe, J. (2005) Principal Component Analysis. Chichester: Wiley.
22. Karhunen, K. (1947) Über lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fenn. A, 37, 1-79.
23. Kneip, A. and Utikal, K. (2001) Inference for density families using functional principal components analysis. J. Am. Statist. Ass., 96, 519-531.
24. Locantore, N., Marron, J. S., Simpson, D. G., Tripoli, N., Zhang, J. T. and Cohen, K. L. (1999) Robust principal component analysis for functional data. Test, 8, 1-73.
25. Loève, M. (1946) Fonctions aléatoires de second ordre. Rev. Sci., 84, 195-206.
26. Panaretos, V. M. and Tavakoli, S. (2013a) Fourier analysis of stationary time series in function space. Ann. Statist., 41, 568-603.
27. Panaretos, V. M. and Tavakoli, S. (2013b) Cramér-Karhunen-Loève representation and harmonic principal component analysis of functional time series. Stoch. Processes Appl., 123, 2779-2807.
28. Politis, D. N. (2011) Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices. Econmetr. Theor., 27, 703-744.
29. Ramsay, J. O. and Dalzell, C. J. (1991) Some tools for functional data analysis (with discussion). J. R. Statist. Soc. B, 53, 539-572.
30. Ramsay, J. and Silverman, B. (2002) Applied Functional Data Analysis. New York: Springer.
31. Ramsay, J. and Silverman, B. (2005) Functional Data Analysis, 2nd edn. New York: Springer.
32. Reiss, P. T. and Ogden, R. T. (2007) Functional principal component regression and functional partial least squares. J. Am. Statist. Ass., 102, 984-996.
33. Shumway, R. and Stoffer, D. (2006) Time Series Analysis and Its Applications, 2nd edn. New York: Springer.
34. Silverman, B. (1996) Smoothed functional principal components analysis by choice of norm. Ann. Statist., 24, 1-24.
35. Stadlober, E., Hörmann, S. and Pfeiler, B. (2008) Quality and performance of a PM10 daily forecasting model. Atmosph. Environ., 42, 1098-1109.
36. Viviani, R., Grön, G. and Spitzer, M. (2005) Functional principal component analysis of fMRI data. Hum. Brain Mappng, 24, 109-129.