A generator of cauchy-distributed time series with specific Hurst index - Estrada-Vargas, Leopoldo; Toral-Cruz, Homero; Pathan, Al-Sakib Khan (2011)
A generator of artificial Cauchy-distributed time series is presented. This generator transforms any random time series, e.g., standardized fractional Gaussian noise (FGN), into a Cauchy-distributed series with specific location and scale parameters and correlation structure, determined by the Hurst index. The proposed algorithm consists of an inverse cumulative distribution function (ICDF) transformation, a wavelet-analysis synthesis and, finally, a linear transformation. The resulting Cauchy-distributed series has approximately the desired location and scale parameters and exactly the desired Hurst index. The performance of the proposed generator is evaluated by estimating the location, scale and Hurst parameters from artificial time series and by calculating the mean squared error (MSE) of their cumulative distribution function (CDF). The input location, scale and Hurst index used in the simulations are taken from jitter samples of monitored Voice over Internet Protocol (VoIP) calls, which have been proved to be adequately modeled with these processes under some circumstances.