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On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root

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  • Park, Chul Gyu
  • Shin, Dong Wan

Abstract

In the autoregressive moving average (ARMA) model with one autoregressive unit root, limiting distribution of the residual autocorrelations depends only on parameters other than the parameter corresponding to the unit root and is the same as that in the corresponding stationary ARMA process. On the other hand, limiting distribution of the partial sum process of residuals does not depend on parameter other than the parameter corresponding to the unit root and is the same as that in AR(1) with autoregressive coefficient one.

Suggested Citation

  • Park, Chul Gyu & Shin, Dong Wan, 1996. "On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 341-346, May.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:4:p:341-346
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    References listed on IDEAS

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    1. Heon Jin Park & Wayne A. Fuller, 1995. "Alternative Estimators And Unit Root Tests For The Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 415-429, July.
    2. Jushan Bai, 1993. "On The Partial Sums Of Residuals In Autoregressive And Moving Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 247-260, May.
    3. Kulperger, R. J., 1985. "On the residuals of autoregressive processes and polynomial regression," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 107-118, December.
    4. Horváth, Lajos, 1993. "Change in autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 221-242, February.
    5. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-459, October.
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