Asymptotic Properties of the LS-estimator of a Gaussian Autoregressive Process by an Averaging Method

作者：Fathallah Hamdi^*

来源：Communications in Statistics - Theory and Methods, 2013, 42(17): 3148-3173.

DOI：10.1080/03610926.2011.621576

• Almost-sure central limit theorem
• Averaging method
• Asymptotic properties of estimators
• Quadratic strong law
• Weighted LS-estimator

This article deals with the problem of parameter estimation of a continuous-time p-dimensional Gaussian autoregressive process. In the stable case, we combine averaging and weighting methods to establish, for the weighted LS-estimator (least-squares estimator) of , an almost-sure central limit theorem (ASCLT), a quadratic strong law (QSL) and a central limit theorem (CLT) associated to the QSL with arithmetic convergence rates. In the unstable case, we establish for the LS-estimator of , the same optimal asymptotic properties with arithmetic convergence rates. In both cases, using the QSL property, we construct a new estimator of the noise covariance sigma(2) and we specify its weak convergence rates.

• 出版日期2013-9-2