1, with T being the sample size and c a fixed constant, 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 square error than the properly specified AR(p + 1) model due to its parsimony. The consequences of this result are: (i) for forecasting purposes it is better to overdifferentiate than to underdifferentiate, (ii) the superiority of the overdifferenced predictor is small in the short term forecast but increases with the horizon, (iii) model selection based on predictive performance can lead to the wrong model in nearly nonstationary autoregression."> 1, with T being the sample size and c a fixed constant, 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 square error than the properly specified AR(p + 1) model due to its parsimony. The consequences of this result are: (i) for forecasting purposes it is better to overdifferentiate than to underdifferentiate, (ii) the superiority of the overdifferenced predictor is small in the short term forecast but increases with the horizon, (iii) model selection based on predictive performance can lead to the wrong model in nearly nonstationary autoregression."> 1, with T being the s">
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Properties of predictors in overdifferenced nearly nonstationary autoregression

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  • Sánchez, Ismael
Abstract
This paper analyzes the effect of overdifferencing a stationary AR(p + 1) process whose largest root is near unity. It is found that if the largest root is p = exp( -cjT(3), f3 > 1, with T being the sample size and c a fixed constant, 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 square error than the properly specified AR(p + 1) model due to its parsimony. The consequences of this result are: (i) for forecasting purposes it is better to overdifferentiate than to underdifferentiate, (ii) the superiority of the overdifferenced predictor is small in the short term forecast but increases with the horizon, (iii) model selection based on predictive performance can lead to the wrong model in nearly nonstationary autoregression.

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  • Sánchez, Ismael, 1995. "Properties of predictors in overdifferenced nearly nonstationary autoregression," DES - Working Papers. Statistics and Econometrics. WS 10347, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10347
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    1. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
    2. Tsay, Ruey S, 1993. "Calculating Interval Forecasts: Comment: Adaptive Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 140-142, April.
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    7. Plosser, Charles I. & Schwert, G. William, 1977. "Estimation of a non-invertible moving average process : The case of overdifferencing," Journal of Econometrics, Elsevier, vol. 6(2), pages 199-224, September.
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    9. Tanaka, Katsuto & Maekawa, Koichi, 1984. "The sampling distributions of the predictor for an autoregressive model under misspecifications," Journal of Econometrics, Elsevier, vol. 25(3), pages 327-351, July.
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    1. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2021. "Spurious relationships in high-dimensional systems with strong or mild persistence," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1480-1497.
    2. Alfredo Garcia Hiernaux & Miguel Jerez & José Casals, 2005. "Unit Roots and Cointegrating Matrix Estimation using Subspace Methods," Documentos de Trabajo del ICAE 0512, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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