Asymptotic analysis of the finite predictor for fractional Gaussian noise
Abstract
This paper proposes a new approach to the asymptotic analysis of the finite predictor for stationary sequences. Our method yields the exact asymptotics of both the relative prediction error and the partial correlation coefficients. The underlying assumptions are analytic in nature, making the approach applicable to processes with long-range dependence. The ARMA-type process driven by fractional Gaussian noise (fGn), which had previously remained elusive, is used as a case study.
Fields of Study & Subjects
Financial Risk and Volatility Modeling
Power Line Communications and Noise
Statistical Methods and Inference
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 4
- Pages
- 3168–3194
- Publication date
- 31 July 2026
- Language
- EN