We analyze the effect of overdifferencing a stationary AR(p + 1) process whose largest root is near unity. It is found that, if the process is nearly nonstationary, the estimators of the overdifferenced model ARIMA(p, 1, 0) are root-T consistent. It is also found that this misspecified ARIMA(p, 1, 0) has lower predictive mean squared error, to terms of small order, than the properly specified AR(p + 1) model due to its parsimony. The advantage of the overdifferenced predictor depends on the remaining roots, the prediction horizon and the mean of the process.