Local asymptotic normality property for fractional Gaussian noise under high-frequency observations

TL;DR

This paper establishes the Local Asymptotic Normality property for fractional Gaussian noise in high-frequency observation regimes, highlighting the necessity of non-diagonal rate matrices for accurate parameter estimation.

Contribution

It proves the LAN property with a non-diagonal rate matrix for fractional Gaussian noise, a novel result differing from existing LAN frameworks.

Findings

LAN property holds with a non-diagonal rate matrix

Non-diagonal rate matrices are essential for fractional Gaussian noise

Results impact high-frequency statistical inference for Gaussian processes

Abstract

Local Asymptotic Normality (LAN) property for fractional Gaussian noise under high-frequency observations is proved with a non-diagonal rate matrix depending on the parameter to be estimated. In contrast to the LAN families in the literature, non-diagonal rate matrices are inevitable.