Moderate deviations principle for empirical covariance from a unit root

Abstract

In the present paper, we consider the linear autoregressive model in $\rr$, $$X_{k,n}={\theta }_n{X}_{k,n-1}+{\xi }_k,k=0,1,...,n,n\ge 1$$ where ${\theta }_n\in [0,1)$ is unknown, $(ξ_k)_{k\in\zz}$ is a sequence of centered i.i.d. r.v. valued in $\rr$ representing the noise. When ${\theta }_n\to 1$, the moderate deviations principle for empirical covariance is discussed and as statistical applications we provide the moderate deviation estimates of the least square and the Yule-Walker estimators of the parameter ${\theta }_n$.

33 pages

Cited by in corpus (1)

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