The paper investigates the estimation bias of autoregressive models for bounded stochastic processes and the performance of the standard procedures in the literature that aim to correcting the estimation bias. It is shown that, in some cases, the bounded nature of the stochastic processes worsen the estimation bias effect, which suggests the design of bound-specific bias correction methods. The paper focuses on two popular autoregressive estimation bias correction procedures which are extended to cover bounded stochastic processes. Finite sample performance analysis of the new proposal is carried out using Monte Carlo simulations which reveal that accounting for the bounded nature of the stochastic processes leads to improvements in the estimation of autoregressive models. Finally, an illustration is given using the current account balance of some developed countries, whose shocks persistence measures are computed.