On the relationship between 1/f and alpha-stable processes

1/f^β-type spectral behavior has received considerable attention in the literature because it arises from a wide range of natural phenomena. In this paper we consider a filtered Poisson process model, and show that this model gives rise to a power-law α-stable process if β<1, or to a process with power-law α-stable increments if 1<β<3. Based on the relationship between α and β we propose a new method for the estimation of the spectral exponent of the sample spectrum, which is particularly robust in the case 0<β<1