MODWTMaximal Overlap Discrete Wavelet Transform
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i) Type of Wavelet Filter and Level of Decomposition: MODWT is used to decompose the weekly National Stock Exchange Fifty index closing price to overcome the limitation of DWT.
ii) Decomposition: MODWT (type: Haar) was used to decompose the National Stock Exchange Fifty index into various subseries also known as wavelets.
series without MODWT decomposition) is modeled and predicted using SVR and ANN models.
The MODWT is a linear filtering operation that transforms a series into coefficients related to variations over a set of scales.
1 MODWT Wavelet Coefficients and Scaling Coefficients
g,I] are jth level MODWT wavelet and scaling filters, defined in terms of the jth-level equivalent wavelet and scaling filters for a discrete wavelet transform (DWT) (for details see [40]).
it] are stationary processes, a MODWT transformation of the two series can be performed to obtain vectors of wavelet coefficients [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
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].
Like the DWT and MODWT described above, the MODWPT coefficients can be used in a multi-resolution analysis to estimate the partition of variance between frequency intervals (the wavelet packet variance) and to test for significant changes in variance across the space for a given packet.
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.