Constructing a quasilinear moving average using the scaling function

The scaling function from multiresolution analysis can be used to constuct a smoothing tool in the context of time series analysis. We give a time series smoothing function for which we show the properties of a quasilinear moving average. Furthermore; we discuss its features and especially derive the distributional properties of our quasilinear moving average given some simple underlying stochastic processes. Eventually we compare it to existing smoothing methods in order to motivate its application