Home > Research > Publications & Outputs > Efficient computation of the discrete autocorre...

Research

Links

Text available via DOI:

Keywords

View graph of relations

Efficient computation of the discrete autocorrelation wavelet inner product matrix.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Efficient computation of the discrete autocorrelation wavelet inner product matrix. / Eckley, Idris A.; Nason, Guy P.
In: Statistics and Computing, Vol. 15, No. 2, 19.04.2005, p. 83-92.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Eckley, IA & Nason, GP 2005, 'Efficient computation of the discrete autocorrelation wavelet inner product matrix.', Statistics and Computing, vol. 15, no. 2, pp. 83-92. https://doi.org/10.1007/s11222-005-6200-y

APA

Eckley, I. A., & Nason, G. P. (2005). Efficient computation of the discrete autocorrelation wavelet inner product matrix. Statistics and Computing, 15(2), 83-92. https://doi.org/10.1007/s11222-005-6200-y

Vancouver

Eckley IA, Nason GP. Efficient computation of the discrete autocorrelation wavelet inner product matrix. Statistics and Computing. 2005 Apr 19;15(2):83-92. doi: 10.1007/s11222-005-6200-y

Author

Eckley, Idris A. ; Nason, Guy P. / Efficient computation of the discrete autocorrelation wavelet inner product matrix. In: Statistics and Computing. 2005 ; Vol. 15, No. 2. pp. 83-92.

Bibtex

@article{528685bd39464fb29a55fe2ebfdedd60,
title = "Efficient computation of the discrete autocorrelation wavelet inner product matrix.",
abstract = "Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inner product matrix using a two-scale property of the a.c. wavelets. The recursive method is an (log (N)3) operation which compares favourably with the (N log N) operations required by the brute force approach. We conclude by describing an efficient construction of the inner product matrix in the (separable) two-dimensional case.",
keywords = "recursive wavelet relation - locally stationary time series - autocorrelation wavelets",
author = "Eckley, {Idris A.} and Nason, {Guy P.}",
note = "RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research",
year = "2005",
month = apr,
day = "19",
doi = "10.1007/s11222-005-6200-y",
language = "English",
volume = "15",
pages = "83--92",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - Efficient computation of the discrete autocorrelation wavelet inner product matrix.

AU - Eckley, Idris A.

AU - Nason, Guy P.

N1 - RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research

PY - 2005/4/19

Y1 - 2005/4/19

N2 - Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inner product matrix using a two-scale property of the a.c. wavelets. The recursive method is an (log (N)3) operation which compares favourably with the (N log N) operations required by the brute force approach. We conclude by describing an efficient construction of the inner product matrix in the (separable) two-dimensional case.

AB - Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inner product matrix using a two-scale property of the a.c. wavelets. The recursive method is an (log (N)3) operation which compares favourably with the (N log N) operations required by the brute force approach. We conclude by describing an efficient construction of the inner product matrix in the (separable) two-dimensional case.

KW - recursive wavelet relation - locally stationary time series - autocorrelation wavelets

U2 - 10.1007/s11222-005-6200-y

DO - 10.1007/s11222-005-6200-y

M3 - Journal article

VL - 15

SP - 83

EP - 92

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -