Generation and prediction of self-similar processes by surrogates

A self-similar process has power spectrum with power law depending on its self-similarity parameter H and we use this property for its generation by the method of surrogate data. The surrogates are a set of random data with the same distribution as that of the increments of the process. These are iteratively rearranged according to the rank order of a time series obtained with the same power law spectrum. The method is fast, and reliable as shown by the characteristics reproduced. It is also possible to extend this method to prediction of a self-similar process, the success of which will depend on the number of available data.