Prediction and estimation for fractal processes using multiscale state-space algorithms

The 1/f family of fractal processes provides useful models for the extraordinary variety of natural and man-made phenomena that exhibit long-term dependence. Using algorithms based on a multiscale-state-space representation, we address the problems of parameter estimation of discrete 1/f signals in white noise, estimation of deterministic signals in 1/f noise, and prediction of discrete 1/f processes. Among other results, distant past data are shown to have a dramatically greater effect on these estimators than when ARMA processes are involved