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6

The issue with any extension method you may use is that it has influence on the coefficents post boundary one way or another. Traditional methods (zero padding, symetric, polynomial extrapolation etc) carry because of the circularity of the wavelet function incluence into the coefficients. You can attempt to use any of the extensions commented if the signal ...


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What you are after are causal wavelets, which is an approach to wavelet filtering that only takes in present and past data. http://soliton.ae.gatech.edu/people/dcsl/papers/aiaa04.pdf


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Wavelets are filters decomposing in a specific number of frequencies a signal across time, they are unique in that they can analyze non-stationary signals (most time series are). They decompose the signal in scaling and detail coefficients (high frequency and low frequency parts). You can attempt to find the true price, meaning the signal, having extracted ...


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It sounds like this is a numerical problem without analytic solution. So I would suggest to use a numerical optimizer to minimize the standard deviation, e.g. MATLABs FMINCON() function can minimize virtually any expression that can be calculated. So for your problem, I recommend to calculate: $$\text{Fmincon}(\sigma(x))$$ where $x$ being your coefficient ...


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Your signal on the edges after denoising will be always altered by the boundary effect of the extension of the data which is incorporated in the reconstruction of the filter as per how wavelets are constructed (take pass and future data) the effect will be greater the longer the filter length you select as it implies more coeficients. Causal wavelets as ...


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