Eckley, Idris A. and Nason, Guy P. (2005) Efficient computation of the discrete autocorrelation wavelet inner product matrix. Statistics and Computing, 15 (2). pp. 83-92. ISSN 0960-3174Full text not available from this repository.
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.
|Journal or Publication Title:||Statistics and Computing|
|Additional Information:||RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research|
|Uncontrolled Keywords:||recursive wavelet relation - locally stationary time series - autocorrelation wavelets|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||29 Mar 2008 15:24|
|Last Modified:||07 Jan 2015 13:54|
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