Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of 1/f Noise Type

A fractal signal x(t) in biomedical engineering may be characterized by 1/f noise, that is, the power spectrum density (PSD) divergences at f = 0. According the Taqqu's law, 1/f noise has the properties of long-range dependence and heavy-tailed probability density function (PDF). The contribution of this paper is to exhibit that the prediction error of a biomedical signal of 1/f noise type is long-range dependent (LRD). Thus, it is heavy-tailed and of 1/f noise. Consequently, the variance of the prediction error is usually large or may not exist, making predicting biomedical signals of 1/f noise type difficult.