Abbreviation: WaveletFilterHaar
Category: Wavelet
Input Parameters:

 
Calculation:

InverseHaarWavelet(ThresholdFilter(HaarWavelet(X,n),T))

Calculates direct Haar wavelet transform of X over the last n points. Applies threshold filter to the result (sets to zero all wavelet coefficients less than T% of the largest one except the Smoothing coefficient; the value of Smoothing (bias) coefficient is always set to zero). Calculates inverse Haar wavelet transform of the result of filtering. Returns the result of the inverse transform corresponding to the current time point.

where

X = Time Series
n = 2^Window Exponent
T = Percent Threshold

 
Discussion:
As the value of the Smoothing (bias) wavelet coefficient is always set to zero, if you call this indicator with Percent Threshold=0, you will get back the input Time Series with zero bias rather than this Time Series itself. Note that the bias is recalculated for each position of the n Periods sized moving window, so it is not a constant through the whole time series. Such type of filtering may be believed to make some internal features of the Time Series, revealed as a result of filtering, more pronounced. While the acceptable range for the Percent Threshold is from 0 to 100%, it is recommended to vary this value from 0 through such values as 0.001 or 0.1 or 0.5 or 1 or 2 up to about 10%. Usually there are only several wavelets with relatively large amplitudes (wavelet coefficients), and most of them are less than several % of the largest one. So, the changes in the filtered picture are most pronounced for low Threshold values. For more information on Wavelets refer to Wavelet Discussion.

For more details, refer to Wavelets and Filter Banks, by Gilbert Strang and Truong Nguyen (Wellesley ‘ Cambridge Press, 1996).