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Efficient Estimation Of Nonstationary Time Series Regression

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  • A. C. Harvey
  • P. M. Robinson

Abstract

. A multiple time series regression model with trending regressors has residuals that are believed to be not only serially dependent but nonstationary. Assuming the residuals can be decomposed as a stationary autoregressive process of known order multiplied by an unknown time‐varying scale factor, we propose estimators of the regression coefficients and show them to be as efficient as estimators based on known scale factors. Our estimators have features in common with adaptive estimators proposed by Carroll (1982) and Hannan (1963) for different regression problems, involving respectively independent residuals with heteroskedasticity of unknown type, and stationary residuals with unknown serial dependence structure.

Suggested Citation

  • A. C. Harvey & P. M. Robinson, 1988. "Efficient Estimation Of Nonstationary Time Series Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 201-214, May.
    • Handle: RePEc:bla:jtsera:v:9:y:1988:i:3:p:201-214
    DOI: 10.1111/j.1467-9892.1988.tb00464.x
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    Cited by:

    1. Zhang, Erhua & Wu, Jilin, 2020. "Adaptive estimation of AR∞ models with time-varying variances," Economics Letters, Elsevier, vol. 197(C).
    2. Yoshihiro Usami & Mituaki Huzii, 1995. "Estimation Of Coefficients Of Time Series Regression With A Nonstationary Error Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 105-118, January.
    3. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    4. Dalla, Violetta & Giraitis, Liudas & Robinson, Peter M., 2020. "Asymptotic theory for time series with changing mean and variance," Journal of Econometrics, Elsevier, vol. 219(2), pages 281-313.

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