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The asymptotic convergence of the parameter estimator in the first order autoregressive model AR(1) under strong mixing errors

Abderrahmane Belguerna, Samir Benaissa


To look in the future in many domain, we are sure that the autoregressive process takes an important place in predicting problems leading to decision making. some studies in reduction of the order of autoregressive model, let the first order autoregressive model more interesting in practise. In this last model we know that the least squares estimator b'n complete converge to unknown parameter ' when the model AR(1) is attached to independent and identically distributed errors "i using the Whittle inequalities. In this paper we show that the least squares estimator complete converge to ' also under strong mixing errors using the moments inequalities and we construct the inequalities of the coefficient of the first order autoregressive model. Using these inequalities a confidence interval is then obtained.


Autoregressive process, strong mixing, parameter estimation, Complete convergence, confidence interval.

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