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Properties Of Predictors In Overdifferenced Nearly Nonstationary Autoregression

Author

Listed:
  • Daniel Peña

    (Universidad Carlos III de Madrid)

  • Ismael Sánchez

    (Universidad de Alicante)

Abstract

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.

Suggested Citation

  • Daniel Peña & Ismael Sánchez, 1999. "Properties Of Predictors In Overdifferenced Nearly Nonstationary Autoregression," Working Papers. Serie AD 1999-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  • Handle: RePEc:ivi:wpasad:1999-08
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    References listed on IDEAS

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    1. Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 253-264, July.
    2. Tsay, Ruey S, 1993. "Testing for Noninvertible Models with Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 225-233, April.
    3. Plosser, Charles I. & Schwert*, G. William, 1978. "Money, income, and sunspots: Measuring economic relationships and the effects of differencing," Journal of Monetary Economics, Elsevier, vol. 4(4), pages 637-660, November.
    4. David F. Findley, 1984. "On Some Ambiguities Associated With The Fitting Of Arma Models To Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(4), pages 213-225, July.
    5. N. Davies & P. Newbold, 1980. "Forecasting with Misspecified Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 87-92, March.
    6. 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.
    7. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
    8. 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.
    9. 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.
    10. Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(4), pages 433-444, December.
    11. A. C. Harvey, 1981. "Finite Sample Prediction And Overdifferencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(4), pages 221-232, July.
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    Cited by:

    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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