MODWTMaximal Overlap Discrete Wavelet Transform
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The MODWT transformation of excess returns of the stocks and market premiums was performed using a Daubechies least asymmetric filter with a wavelet filter length of 8 (LA8).
We tested the CAPM for raw returns (in this CAPM model, the betas in the first step were obtained on raw, MODWT non-transformed, returns), and for return dynamics of wavelet scales [[tau].
Another thorough description of MODWT using matrix algebra is found in Gencay et al.
3) Percival and Walden (2000) denote scales of MODWT obtained wavelet coefficients with a letter t and scales of scaling coefficients with X.
Lark and Webster (2004) showed how the MODWT analysis can be extended to 2 dimensions.
We used the MODWT in 1 and 2 dimensions and the MODWPT to investigate the data from the 2 aerial photographs.
This last result supports the above observation on the MODWT wavelet variance, where we saw that the relative contribution of the 64-128 pixel scale variation is inflated compared to the other transects.