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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.

computational and mathematical methods in medicine

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>f</mml:mi></mml:math>Noise Type

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of1/fNoise Type