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Regression with a Slowly Varying Regressor in the Presence of a Unit Root

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  • Yoshimasa Uematsu
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    Abstract

    This paper considers the regression model with a slowly varying (SV) regressor in the presence of a unit root in serially correlated disturbances. This regressor is known to be asymptotically collinear with the constant term; see Phillips (2007). Under nonstationarity, we find that the estimated coefficients of the constant term and the SV regressor are asymptotically normal, but neither is consistent. Further, we derive the limiting distribution of the unit root test statistic. We may here observe that the finite sample approximation to the limiting one is not monotone and it is poor due to the influence of the collinear regressor. In order to construct a well-behaved test statistic, we recommend dropping the constant term intentionally from the regression and computing the statistics, which are still consistent under the true model having the constant term. The powers and sizes of these statistics are found to be well-behaved through simulation studies. Finally, these results are extended to general Phillips and Perron-type statistics.

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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd11-209.pdf
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    Bibliographic Info

    Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd11-209.

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    Date of creation: Oct 2011
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    Handle: RePEc:hst:ghsdps:gd11-209

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    1. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
    2. Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers 10353, Iowa State University, Department of Economics.
    3. Pierre Perron & Tomoyoshi Yabu, 2005. "Estimating Deterministric Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-037, Boston University - Department of Economics.
    4. Mynbaev, Kairat T., 2009. "Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion," Econometric Theory, Cambridge University Press, vol. 25(03), pages 748-763, June.
    5. Phillips, Peter C.B. & Sun, Yixiao, 2003. "02.3.1. Regression with an Evaporating Logarithmic Trend Solution," Econometric Theory, Cambridge University Press, vol. 19(04), pages 692-701, August.
    6. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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