Forecasting an ARIMA (0,2,1) using the random walk model with drift

In this paper we show that the random walk model with drift behaves like an ARIMA (0,2,1) when its parameter θ is greater but close to –1. Using the random walk for predicting future values of an ARIMA (0,2,1) process, we find out that when θ is not so close to –1, the performance of the prediction interval for the period forecast is not satisfactory. Particularly, for large, the achieved coverage, namely, the probability the prediction interval to include the future value is quite low. Even in the cases of large samples and small , although the random walk coverage approaches that of the ARIMA, the random walk produces wider prediction intervals. This picture changes when we forecast ARIMA (0,2,1) values for θ close to –1. The random walk should be preferred as it produces on average narrower confidence intervals, and its coverage is almost the same with the nominal coverage of the ARIMA (0,2,1).