Moderate deviations principle for empirical covariance from a unit root

2012/07/17 by Yu Miao, Yanling Wang, Miao, Yu +3
Economics, Econometrics and Finance · Mathematics · #60F10 #60G10 #62J05 #FOS: Mathematics #Financial Risk and Volatility Modeling #Monetary Policy and Economic Impact #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1207.4031

openalex publication_date 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we consider the linear autoregressive model in \rr, X_k,n=θ_n X_k,n-1+ξ_k, k=0,1,...,n, n≥ 1 where θ_n∈ [0,1) is unknown, (ξ_k)_k∈\zz is a sequence of centered i.i.d. r.v. valued in \rr representing the noise. When θ_n→ 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 θ_n.

Citations

• Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root

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