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Bootstrapping Spurious Regression

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Abstract

The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even first order consistent. The block bootstrap serial correlation coefficient does converge to unity and is therefore first order consistent, but has a slower rate of convergence and a different limit distribution from that of the sample data serial correlation coefficient. The analysis covers spurious regressions involving both deterministic trends and stochastic trends. The results reinforce earlier warnings about routine use of the bootstrap with dependent data.

Suggested Citation

  • Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1330
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    References listed on IDEAS

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    1. Hinkley, D. V., 1997. "Discussion of paper by H. Li & G.S. Maddala," Journal of Econometrics, Elsevier, vol. 80(2), pages 319-323, October.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Horowitz, Joel L., 1999. "The Bootstrap," Working Papers 99-10, University of Iowa, Department of Economics.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
    6. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
    7. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    8. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    9. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    10. 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.
    11. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
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    1. Phillips, Peter C.B., 2010. "Bootstrapping I(1) data," Journal of Econometrics, Elsevier, vol. 158(2), pages 280-284, October.
    2. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Carsten Jentsch & Dimitris N. Politis & Efstathios Paparoditis, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 416-441, May.
    3. Anindya Banerjee & Josep Lluís Carrion-i-Silvestre, 2006. "Cointegration in Panel Data with Breaks and Cross-Section Dependence," Economics Working Papers ECO2006/5, European University Institute.
    4. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
    5. Imed Drine & Christophe Rault, 2008. "Purchasing Power Parity For Developing And Developed Countries. What Can We Learn From Non‐Stationary Panel Data Models?," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 752-773, September.
    6. Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers 14-18, University of Mannheim, Department of Economics.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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