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There have been found potential problems occurred on the classical wavelet methods during the transformation process from the infinite signal to a treated boundary problems the wavelet regression. A simple method to minimize bias at the boundaries is proposed in this study. This method basically combined the two methods of local linear quantile regression and wavelet functions (WR-LLQ). However, this technique will be used to predict the stock index time series. The combination of WR-LLQ methods are compared through experimental data carried out in this research. The main finding of this study is the enhancement of prediction of stock ending-prices compares to previous models. Wavelet regression is a new non parametric method characterized by the ability to detect unusual appearances, which might be observed in noisy data. Tendency, collapse points, and discontinuities can be taken into consideration by wavelet methods, but when performing wavelet regression it is usual to consider some f boundary assumptions, such as periodicity or symmetry. However, such assumptions may not always be logical to treat this problem, it is suggested by Oh, Naveau, and Lee (2001) to split f as the sum of a set of wavelet basis functions, fw, plus a low-order polynomial, fp. So f = fw+fp. The hope is that, once fp is removed from f, the remaining portion f_w can be well estimated using wavelet regression with the said periodic boundary assumption. Practically, this approach requires choosing of the polynomial order for fp and the wavelet thresholding value for fw. Lee, Oh (2004), Naveau, and Oh (2003) propose a simple method called polynomial wavelet regression (PWR) for handling these boundary problems. Oh and Lee (2005) proposed a method for correcting the boundary bias, they join wavelet shrinkage with local polynomial regression, where the latter regression technique known of a perfect boundary properties. Simulation results from both the univariate and bivariate settings provide strong evidence that the proposed method is very successful in terms of rectify boundary bias.
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