In this article, some methods of estimation such as ordinary least squares (OLS), modification for least squares (MLS), weighted symmetric (WS), modified weighted symmetric (MWS) and maximum likelihood (ML) are introduced for the first order autoregressive model (AR(1)) with a unit root. Also, the properties of OLS estimator are discussed. A comparative study between these methods is considered in the case of unit root and explosive time series, using Monte Carlo simulation.

unit roots estimators, explosive time series, AR(1) model,MLS method, MWS method.