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Estimation of the Trend Model with Autoregressive Errors

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  • Roy, Anindya
  • Falk, Barry
  • Fuller, Wayne A.

Abstract

This paper is concerned with estimation and inference in a univariate p-th order autoregressive model with a time trend and, possibly, a unit root. Econometric interest in uni variate autoregressions is partly due to the direct benefits that are attainable from a better understanding of the time series structures of individual economic variables. In addition, developments in the study of univariate time series typically lead the way to developments in the study of multivariate time series models. There are two fundamental problems that complicate estimation and inference in autoregressive models with a possible unit root (i.e., AR/UR models). First, the ordinary least squares (OLS) estimator is biased and nonnormal in finite samples. Second, the asymptotic distribution of the OLS estimator is discontinuous at the boundary of the parameter space, being normal in the interior but nonstandard at the unit root endpoint.

Suggested Citation

  • Roy, Anindya & Falk, Barry & Fuller, Wayne A., 1999. "Estimation of the Trend Model with Autoregressive Errors," ISU General Staff Papers 199907010700001328, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genstf:199907010700001328
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    References listed on IDEAS

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    1. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
    2. Falk, Barry & Roy, Anindya, 1999. "Efficiency Tradeoffs in Estimating the Trend and Error Structure of the Linear Model," ISU General Staff Papers 199908010700001327, Iowa State University, Department of Economics.
    3. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    4. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
    5. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    6. DeJong, David N. & Whiteman, Charles H., 1991. "Reconsidering 'trends and random walks in macroeconomic time series'," Journal of Monetary Economics, Elsevier, vol. 28(2), pages 221-254, October.
    7. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    8. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
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    Cited by:

    1. Falk, Barry & Roy, Anindya, 1999. "Efficiency Tradeoffs in Estimating the Trend and Error Structure of the Linear Model," ISU General Staff Papers 199908010700001327, Iowa State University, Department of Economics.

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