Predictors for the discrete time fractional Gaussian processes

A discrete-time k-step predictor for fractional Gaussian noise is presented. Theoretical and simulated values of the normalized mean-square error are presented. Rules of thumb (Norros, 1995) are verified but in discrete time prediction. Furthermore, we deal with the problem of finding an estimate for the Hurst parameter H of the fractional Brownian motion (FBM) and with the problem of obtaining a complete prediction for the increments of the FBM in different instants and scales of time. We show that the wavelet analysis of the FBM is an appropriate tool for solving both of these problems. Several simulations are presented and comparisons with theoretical values are shown