Wavelet analysis of matrix–valued time–series
Andrew T. Walden, Abdeslam Serroukh · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2002
The construction of matrix–valued filters for multi–resolution analysis of matrix–valued time–series is studied. Several different designs are explicitly derived corresponding to perfect reconstruction orthonormal filter banks. The resulting matrixvalued scaling functions and wavelet functions are calculated. Two of the derived filter classes have variable parameters providing rich classes of designs. A discrete matrix–valued wavelet transform and inverse transform is fully described and applied to a 2 × 2 time–series of daily bond yields. It is demonstrated that this series can be reconstructed to a very high approximation accuracy using just a small percentage of retained coefficient matrices, both when the retained coefficient matrices are chosen by size of their norm, or by transform level. Possible uses of such matrix–valued multi–resolution analysis include privacy systems and scalable and progressive coding schemes.