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Hyper-Consistent Estimation of a Unit Root in Time Series Regression

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Abstract
It is shown that the fully modified ordinary least squares (FM-OLS) estimator of a unit root in time series regression is T^{3/2}-consistent. Relative to FM-OLS, therefore, the least squares and maximum likelihood estimators are infinitely deficient asymptotically. Simulations show that this dominance of FM-OLS persists even in small samples.

Suggested Citation

  • Peter C.B. Phillips, 1992. "Hyper-Consistent Estimation of a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 1040, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1040
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1040.pdf
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    References listed on IDEAS

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    1. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    4. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

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    2. Helmi Hamdi & Ali Said & Rashid Sbia, 2015. "Empirical Evidence on the Long-Run Money Demand Function in the Gulf Cooperation Council Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 5(2), pages 603-612.
    3. Nasri Harb, 2004. "Money demand function: a heterogeneous panel application," Applied Economics Letters, Taylor & Francis Journals, vol. 11(9), pages 551-555.
    4. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    5. Judith A. Giles & Sadaf Mirza, 1999. "Some Pretesting Issues on Testing for Granger Noncausality," Econometrics Working Papers 9914, Department of Economics, University of Victoria.
    6. Nasri Harb, 2007. "Trade between Euro zone and Arab countries: a panel study," Applied Economics, Taylor & Francis Journals, vol. 39(16), pages 2099-2107.
    7. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, March.

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