Precise Asymptotic Behaviors Of Parameter Estimator In Gaussian Autoregressive Process

Probability focuses on studying regularity of random phenomenon, which is extensively usedin natural science, technological science, social science and managerial science and so on. Hence, ithas been developing rapidly since1930’s and many new branches have emerged from time to time.Probability limit theory is one of the branches and also an important theoretical basis of Probabilityand Statistics. Moreover, during the past40years, the investigation of complete convergence andstrong convergence which are widely used, has become a hot and important field.Based on describing precise asymptotic behaviors of independent identically distributedrandom variable sequence in detail, this paper has been devoted to precise asymptotic behaviors of theleast-squares estimator in the Gaussian autoregressive process. At first, by the methods ofBerry-Esseen bound and deviation inequality for the least-squares estimator, we can get the preciseconvergence in the law of iterated logarithm. Secondly,L2-convergence rate of this estimator andnonuniform Berry-Esseen bound for martingales are studied. Then, we can get two kinds of completemoment convergence of this estimator with regard to the first moment and the second moment.