Long-range dependence and rational Gaussian noise

We propose a new time series model called Rational Gaussian Noise (rGn) to describe a pattern of long-range dependence. The rGn model is shown to be an extension of the traditional fractional Gaussian noise (fGn). Theoretical formulas such as autocorrelation function, and some properties of rGn are derived and compared to that of fGn. Transformed S&P500 daily excessive return data is used as a case study where parameters for both the rGn and fGn models are estimated.