Forecasting the stationary AR(1) with an almost unit root

Abstract

Although unit root tests have made a great contribution in time series econometrics, their major disadvantage is the low powers they attain on certain occasions, as for the case of the stationary AR(1), when φis close to one. In this study, considering the random walk as the true model, we derive the probability of the prediction interval to include any future value y_{T + s} of AR(1). Using certain estimates from Monte Carlo simulations, we proceed to numerical computations, resulting in the main finding that the values for the specific probability depend upon the location the most recent available observation in the sample possesses in its marginal distribution.