Moderate deviations principle for empirical covariance from a unit root

Yu Miao, Yanling Wang, Guangyu Yang

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, $(ξ_k)_{k\in\zz}$ i…