A STATISTICAL REASON FOR THE APPEARANCE OF 1/F SPECTRA FROM NOT PERFECTLY CONTINUOUS PROCESSES

摘要

The objective of this paper is the derivation of the spectral estimate for data from a stochastic process that does not perfectly match the common supposition of stochastic continuity. The used model is a Randomly Indexed Random Walk that supposes the data of every sampling interval as the sum of a finite random number of random independent increments. This corresponds to the discreteness of the state space of electron devices. Random increments indicate the transitions between the current state and a randomly selected next one. Transitions are pointlike events occurring at random instants in time. Randomness in time influences the stochastic properties of the recorded data in such a way that the fixed variance of single random increments turns into a random one of the equidistantly recorded data. Thus, despite of the independence of increments, the data appear as positively correlated. The standard spectral estimate yields the 1/f pattern if the random variance component approaches the magnitude of the fixed variance component.