Two general models that generate long range correlation

In this paper we study two models that generate sequences with LRC (long range correlation). For the IFT (inverse Fourier transform) model, our conclusion is the low frequency part leads to LRC, while the high frequency part tends to eliminate it. Therefore, a typical method to generate a sequence with LRC is multiplying the spectrum of a white noise sequence by a decaying function. A special case is analyzed: the linear combination of a smooth curve and a white noise sequence, in which the DFA plot consists of two line segments. For the patch model, our conclusion is long subsequences leads to LRC, while short subsequences tend to eliminate it. Therefore, we can generate a sequence with LRC by using a fat-tailed PDF (probability distribution function) of the length of the subsequences. A special case is also analyzed: if a patch model with long subsequences is mixed with a white noise sequence, the DFA plot will consist of two line segments. We have checked known models and actual data, and found they are all consistent with this study.