Properties of Predictors in Overdifferenced Nearly Nonstationary Autoregression

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

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