A comparative study of two biorthogonal wavelet transforms in time series prediction

We present comparative results of time-series prediction preprocessed with two different wavelet transforms: (1) the compactly supported biorthogonal wavelet transform developed by Cohen, Daubechies, and Feauveau (1992), and (2) the semi-orthogonal wavelet transform, a class of biorthogonal wavelet transform, constructed by Cai and Wang (1996). Both theoretical and computational results of the two wavelet transforms are discussed. The major difference between the two wavelet transforms is the computational procedure. So far, only the semi-orthogonal wavelet transform of Cai and Wang can compute wavelet coefficients from a coarse scale level to a fine scale level, which makes the computation more flexible and cost effective. However, the compactly supported biorthogonal wavelet transform of Cohen et al. Has better decorrelation property. Thus, we found that the semi-orthogonal wavelet transform of Cai and Wang provides a faster computation process while the compactly supported biorthogonal wavelet transform provides better predicted wavelet coefficients in our experimental results. Based on the wavelet coefficients computed from signals, nonlinear prediction models utilizing recurrent neural networks are applied to predict wavelet coefficients at each scale level, Thus, the predicted signal is obtained from the reconstruction of predicted wavelet coefficients, In our experiments, the multi-step prediction using wavelet transforms gives much superior results than those obtained without using wavelet transforms. We applied our method to predict specific time series, intracranial pressure, acquired from head-trauma patients in the neuro intensive care unit at the University of Pittsburgh Medical Center