The effects of order misspecification in nonstationary autoregressive time series estimations are investigated. The true process is assumed to be stationary if differenced. The ordinary least squares estimator is shown to be weakly convergent and its probability limit is derived. Expressions for the dominating terms of the prediction error and of the prediction mean squared error are derived. Using the expressions and Monte Carlo simulations, we compare prediction errors in the misspecified models based on the observation series and those based on the differenced series.
- Nonstationary time series
- Prediction mean squared error
- Unit root