Long-range dependence and rational Gaussian noise

Abstract

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.

Keywords:

• Long-range dependence
• rational Gaussian noise
• fractional Gaussian noise
• S&P 500 daily return

2020 Mathematics Subject Classifications:

• 62-08
• 62E10
• 62M10
• 62P05

Disclosure statement

No potential conflict of interest was reported by the author(s).