Abstract
One of the key features of wavelet analysis is its ability to decompose non-stationary signals according to time and scale. In this work, we use discrete wavelets to analyze the influence of detrending techniques on the time-scale information structure of daily financial data. We examine the use of log returns, a linear trend and the Hodrick–Prescott (HP) filter. Quantitative measurements of information distortion are given using the mean-squared error (MSE) and correlation of the wavelet coefficients between the detrended and original data. We find that log returns and linear detrending are most distortional. We also conclude that the HP-filter is most effective, depending on appropriate selection of the filter parameter, λ, which is [Formula: see text] for the given data set.
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