2 research outputs found
Simulation of Gegenbauer Processes using Wavelet Packets
In this paper, we study the synthesis of Gegenbauer processes using the
wavelet packets transform. In order to simulate a 1-factor Gegenbauer process,
we introduce an original algorithm, inspired by the one proposed by Coifman and
Wickerhauser [1], to adaptively search for the best-ortho-basis in the wavelet
packet library where the covariance matrix of the transformed process is nearly
diagonal. Our method clearly outperforms the one recently proposed by [2], is
very fast, does not depend on the wavelet choice, and is not very sensitive to
the length of the time series. From these first results we propose an algorithm
to build bases to simulate k-factor Gegenbauer processes. Given its practical
simplicity, we feel the general practitioner will be attracted to our
simulator. Finally we evaluate the approximation due to the fact that we
consider the wavelet packet coefficients as uncorrelated. An empirical study is
carried out which supports our results