Bernstein-Fréchet inequalities for the parameter of the ordre 1 autoregressive process

by Abdelnasser. DAHMANI & Megdouda. TARI.

Abstract: The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter of the autoregressive process. In the case of the order one autoregressive process we know that the least squares estimator converge in probability to the unknown parameter (. In this work we show that the least squares estimator converge almost surely to ( and so we construct the inequalities of type Bernstein-Fréchet for the coefficient of the order 1 autoregressive process. Using these inequalities a confidence interval is then obtained.

Key Words: Autoregressif Process, Exponentielles Inequalities, Confidence Interval, White Noise

Authors:
Abdelnasser Dahmani, a_dahmany@yahoo.fr
Megdouda Tari, megtari@yahoo.fr

Editor: Di Lorenzo, Renato, rdlea@libero.it

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