Classical wavelet thresholding methods (WTM) is
used to analyze both the non-stationary and nonlinear time
series. Yet, the bounded support of underlain time series
limited the availability of the partial data within its
boundaries. In addition, large biases at the edges was occurred
by increasing the bias when a time series data is defined in
(WTM) which also result in creating artificial wggles. This
study suggests a new two-stage method to concurrently
minimize the effect of the boundaries found in (WTM). Local
Linear Quantile Regression (LLQ) is applied in early stage in
order to provide more accurate description of damaged or
noisy data. However, it is assumed that there will be a
remaining series hidden in the residuals. At second stage
(WTM) has been applied to the residuals. The final stage is the
summation of the fitting estimated from both LLQ and (WTM).
To assess the practical performance of the proposed method a
simulation was run which shows that the optimized WTM
could overcome the classical method used in non-stationary
and nonlinear time series analysis.