메뉴 건너뛰기




Volumn 123, Issue 7, 2013, Pages 2779-2807

Cramér-Karhunen-Loève representation and harmonic principal component analysis of functional time series

Author keywords

Cumulants; Discrete Fourier transform; Functional data analysis; Functional principal components; Mixing; Spectral density operator; Spectral representation

Indexed keywords

DISCRETE FOURIER TRANSFORMS; EIGENVALUES AND EIGENFUNCTIONS; MIXING; SPECTRAL DENSITY; TIME SERIES; TIME SERIES ANALYSIS;

EID: 84885037860     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2013.03.015     Document Type: Article
Times cited : (91)

References (38)
  • 1
    • 84873374810 scopus 로고    scopus 로고
    • Sampled forms of functional pca in reproducing kernel hilbert spaces
    • A.A. Amini, M.J. Wainwright, Sampled forms of functional PCA in reproducing kernel Hilbert spaces, Annals of Statistics 40 (5) (2012) 2452-2482.
    • (2012) Annals of Statistics , vol.40 , Issue.5 , pp. 2452-2482
    • Amini, A.A.1    Wainwright, M.J.2
  • 2
    • 0001181674 scopus 로고
    • Principal components-analysis of sampled functions
    • P. Besse, J.O. Ramsay, Principal components-analysis of sampled functions, Psychometrika 51 (1986) 285-311.
    • (1986) Psychometrika , vol.51 , pp. 285-311
    • Besse, P.1    Ramsay, J.O.2
  • 3
    • 33645031454 scopus 로고
    • Propriétés des opérateurs de covariance empiriques d'un processus stationnaire Hilbertien
    • D. Bosq, Propriétés des opérateurs de covariance empiriques d'un processus stationnaire Hilbertien, Comptes Rendus de l'Académie des Sciences. Série I 309 (14) (1989) 873-875.
    • (1989) Comptes Rendus de l'Académie des Sciences. Série i , vol.309 , Issue.14 , pp. 873-875
    • Bosq, D.1
  • 4
    • 85030496516 scopus 로고
    • Modèle autorégressif Hilbertien application à la prévision du comportement d'un processus á temps continu sur un intervalle de temps donné
    • D. Bosq, Modèle autorégressif Hilbertien, application à la prévision du comportement d'un processus á temps continu sur un intervalle de temps donné, Comptes Rendus de l'Académie des Sciences. Série I 310 (11) (1990) 787-790.
    • (1990) Comptes Rendus de l'Académie des Sciences. Série i , vol.310 , Issue.11 , pp. 787-790
    • Bosq, D.1
  • 5
    • 25144465434 scopus 로고    scopus 로고
    • Estimation of mean and covariance operator of autoregressive processes in banach spaces
    • 10.1023/A:1021279131053
    • D. Bosq, Estimation of mean and covariance operator of autoregressive processes in Banach spaces, Statistical Inference for Stochastic Processes 5 (2002) 287-306. 10.1023/A:1021279131053.
    • (2002) Statistical Inference for Stochastic Processes , vol.5 , pp. 287-306
    • Bosq, D.1
  • 9
    • 84968484391 scopus 로고
    • Kernels of trace class operators
    • C. Brislawn, Kernels of trace class operators, in: Proc. Am. Math. Soc, vol. 104, 1988, pp. 1181-1190.
    • (1988) Proc. Am. Math. Soc , vol.104 , pp. 1181-1190
    • Brislawn, C.1
  • 10
    • 0001469917 scopus 로고    scopus 로고
    • Nonparametric estimation of smoothed principal components analysis of sampled noisy functions
    • H. Cardot, Nonparametric estimation of smoothed principal components analysis of sampled noisy functions, Journal of Nonparametric Statistics 12 (2000) 503-538.
    • (2000) Journal of Nonparametric Statistics , vol.12 , pp. 503-538
    • Cardot, H.1
  • 11
    • 34547277358 scopus 로고    scopus 로고
    • Conditional functional principal components analysis
    • H. Cardot, Conditional functional principal components analysis, Scandinavian Journal of Statistics 34 (2) (2007) 317-335.
    • (2007) Scandinavian Journal of Statistics , vol.34 , Issue.2 , pp. 317-335
    • Cardot, H.1
  • 13
    • 0000957849 scopus 로고
    • Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
    • J. Dauxois, A. Pousse, Y. Romain, Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference, Journal of Multivariate Analysis 12 (1982) 136-154.
    • (1982) Journal of Multivariate Analysis , vol.12 , pp. 136-154
    • Dauxois, J.1    Pousse, A.2    Romain, Y.3
  • 14
    • 0003591656 scopus 로고    scopus 로고
    • Vector integration and stochastic integration in banach spaces
    • Wiley, New York
    • N. Dinculeanu, Vector Integration and Stochastic Integration in Banach Spaces, in: Pure and Applied Mathematics, Wiley, New York, 2000.
    • (2000) Pure and Applied Mathematics
    • Dinculeanu, N.1
  • 16
    • 0000360828 scopus 로고
    • Stochastic processes and statistical inference
    • U. Grenander, Stochastic processes and statistical inference, Arkiv för Matematik 1 (1950) 195-277.
    • (1950) Arkiv för Matematik , vol.1 , pp. 195-277
    • Grenander, U.1
  • 20
    • 33747153005 scopus 로고    scopus 로고
    • Properties of principal component methods for functional and longitudinal data analysis
    • DOI 10.1214/009053606000000272
    • P. Hall, H.G. Müller, J.L. Wang, Properties of principal component methods for functional and longitudinal data analysis, Annals of Statistics 34 (3) (2006) 1493-1517. (Pubitemid 44231170)
    • (2006) Annals of Statistics , vol.34 , Issue.3 , pp. 1493-1517
    • Hall, P.1    Muller, H.-G.2    Wang, J.-L.3
  • 21
    • 77951495664 scopus 로고    scopus 로고
    • Weakly dependent functional data
    • S. Hörmann, P. Kokoszka, Weakly dependent functional data, Annals of Statistics 38 (3) (2010) 1845-1884.
    • (2010) Annals of Statistics , vol.38 , Issue.3 , pp. 1845-1884
    • Hörmann, S.1    Kokoszka, P.2
  • 22
    • 84870657482 scopus 로고    scopus 로고
    • Inference for functional data with applications
    • Springer, New York, NY
    • L. Horváth, P. Kokoszka, Inference for Functional Data with Applications, in: Springer Series in Statistics, Springer, New York, NY, 2012.
    • (2012) Springer Series in Statistics
    • Horváth, L.1    Kokoszka, P.2
  • 24
  • 25
    • 78149287743 scopus 로고
    • Principal components of random variables with values in a seperable hilbert space
    • J. Kleffe, Principal components of random variables with values in a seperable Hilbert space, Mathematische Operationsforschung Statistik 4 (5) (1973) 391-406.
    • (1973) Mathematische Operationsforschung Statistik , vol.4 , Issue.5 , pp. 391-406
    • Kleffe, J.1
  • 29
    • 0036209018 scopus 로고    scopus 로고
    • Weak convergence for the covariance operators of a hilbertian linear process
    • A. Mas, Weak convergence for the covariance operators of a Hilbertian linear process, Stochastic Processes and their Applications 99 (2002) 117-135.
    • (2002) Stochastic Processes and Their Applications , vol.99 , pp. 117-135
    • Mas, A.1
  • 30
    • 33749479351 scopus 로고    scopus 로고
    • Perturbation approach applied to the asymptotic study of random operators
    • Birkhäuser
    • A. Mas, L. Menneteau, Perturbation approach applied to the asymptotic study of random operators, in: High Dimensional Probability III, vol. 55, Birkhäuser, 2003, pp. 127-133.
    • (2003) High Dimensional Probability III , vol.55 , pp. 127-133
    • Mas, A.1    Menneteau, L.2
  • 32
    • 84879130814 scopus 로고    scopus 로고
    • Fourier analysis of stationary processes in function space
    • (in press)
    • V.M. Panaretos, S. Tavakoli, Fourier analysis of stationary processes in function space, Annals of Statistics, 2013, (in press).
    • (2013) Annals of Statistics
    • Panaretos, V.M.1    Tavakoli, S.2
  • 35
    • 0001597980 scopus 로고
    • Estimating the mean and covariance structure nonparametrically when the data are curves
    • J.A. Rice, B. Silverman, Estimating the mean and covariance structure nonparametrically when the data are curves, Journal of the Royal Statistical Society. Series B 53 (1) (1991) 233-243.
    • (1991) Journal of the Royal Statistical Society. Series B , vol.53 , Issue.1 , pp. 233-243
    • Rice, J.A.1    Silverman, B.2
  • 36
    • 0030537857 scopus 로고    scopus 로고
    • Smoothed functional principal components analysis by choice of norm
    • B.W. Silverman, Smoothed functional principal components analysis by choice of norm, Annals of Statistics 24 (1) (1996) 1-24.
    • (1996) Annals of Statistics , vol.24 , Issue.1 , pp. 1-24
    • Silverman, B.W.1
  • 37
    • 0004307223 scopus 로고    scopus 로고
    • Stochastic calculus and financial applications
    • (Corr. 3rd printing ed.), Springer, New York
    • J.M. Steele, Stochastic Calculus and Financial Applications (Corr. 3rd printing ed.), in: 3rd corr. pr of Stochastic Modelling and Applied Probability, vol. 45, Springer, New York, 2003.
    • (2003) 3rd Corr. Pr of Stochastic Modelling and Applied Probability , vol.45
    • Steele, J.M.1
  • 38
    • 19744375466 scopus 로고    scopus 로고
    • Functional data analysis for sparse longitudinal data
    • DOI 10.1198/016214504000001745
    • F. Yao, H.G. Müller, J.L. Wang, Functional data analysis of sparse longitudinal data, Journal of the American Statistical Association 100 (2005) 577-590. (Pubitemid 40816595)
    • (2005) Journal of the American Statistical Association , vol.100 , Issue.470 , pp. 577-590
    • Yao, F.1    Muller, H.-G.2    Wang, J.-L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.