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