Statistical modelling of time series using non-decimated waveletrepresentations
Guy P. Nason, Theofanis Sapatinas, Andrew Sawczenko · 1997
This article proposes the use of time-ordered non-decimated wavelet or nondecimated wavelet packet coefficients to provide a representation of a time series (explanatory). The resulting representations are then used as variables in a statistical model to provide predictions of another time series (response). The statistical model provides valuable information about which components in the explanatory time series drive the response time series. To represent our time series we use a collection of basis functions known as wavelet packets. Our methodology modifies the standard wavelet packets representation by providing an over-determined representation of shifted wavelet packets where the shifts are not restricted to the usual wavelet grid. We introduce a fast algorithm for carrying out the time-ordered non-decimated wavelet packet transform. The shifted wavelet packet bases can represent many classes of time series sparsely. The sparsity provides an effective dimension reduction which en...