2025/04/02 by P. Chigansky, Chigansky, P., M. Kleptsyna +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Power Line Communications and Noise #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #msc:60G22 #msc:60G25 #stat.TH
paper · pdf · doi:10.48550/arxiv.2504.01562
published as Bernoulli 2026, Vol. 32, No. 4, 3168-3194
openalex publication_date 2025/04/02 · openalex created_date 2025/10/10 · arxiv created 2026/06/10 · openalex updated_date 2026/07/28 · arxiv updated 2026/08/04
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.