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Understanding Spurious Regression in Financial Economics

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Author Info
Ai Deng () (Department of Economics, Boston University)

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Abstract

This paper provides an asymptotic theory for the spurious regression analyzed by Ferson, Sarkissian and Simin (2003). The asymptotic framework developed by Nabeya and Perron (1994) is used to provide approximations for the various estimates and statistics. Also, using a fixed-bandwidth asymptotic framework, a convergent t test is constructed, following Sun (2005). These are shown to be accurate and to explain the simulation findings in Ferson et al. (2003). Monte Carlo studies show that our asymptotic distribution provides a very good finite sample approximation for sample sizes often encountered in finance. Our analysis also reveals an important potential problem in the theoretical hypothesis testing literature on predictability. A possible reconciling interpretation is provided.

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Publisher Info
Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2005-048.

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Length: 39 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:bos:wpaper:wp2005-048

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Related research
Keywords: spurious regression observational equivalence Nabeya-Perron asymptotics fixed-b asymptotics data mining nearly integrated nearly white noise (NINW)

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References listed on IDEAS
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  1. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  2. Christopher L. Cavanagh & Graham Elliott & James Stock, 1995. "Inference in Models with Nearly Integrated Regressors," University of California at San Diego, Economics Working Paper Series 95-29, Department of Economics, UC San Diego.
  3. Markku Lanne, 2002. "Testing The Predictability Of Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 407-415, August. [Downloadable!] (restricted)
    Other versions:
  4. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-54, November. [Downloadable!] (restricted)
    Other versions:
  5. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, September. [Downloadable!]
  6. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2003. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," Cowles Foundation Discussion Papers 1407, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  7. Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation, Yale University. [Downloadable!]
  8. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Estimation of Autoregressive Roots Near Unity Using Panel Data," Cowles Foundation Discussion Papers 1224, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  9. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(1), pages 41-66. [Downloadable!] (restricted)
    Other versions:
  10. Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001. "How To Estimate Autoregressive Roots Near Unity," Econometric Theory, Cambridge University Press, vol. 17(01), pages 29-69, February. [Downloadable!]
    Other versions:
  11. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Technical Working Papers 0100, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  12. Walter Torous & Rossen Valkanov, 2000. "Boundaries of Predictability: Noisy Predictive Regressions," University of California at Los Angeles, Anderson Graduate School of Management 1081, Anderson Graduate School of Management, UCLA. [Downloadable!]
  13. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
    Other versions:
  14. Nabeya, S. & Perron, P., 1991. "Local Asymtotic Distributions Related to the AR(1) MOdel with Dependent Errors," Papers 362, Princeton, Department of Economics - Econometric Research Program.
    Other versions:
  15. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July. [Downloadable!] (restricted)
  16. Yakov Amihud & Clifford Hurvich, 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Econometrics 0412008, EconWPA. [Downloadable!]
  17. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  18. repec:cup:etheor:v:10:y:1994:i:3-4:p:672-700 is not listed on IDEAS
  19. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Blackwell Publishing, vol. 63(3), pages 435-63, July. [Downloadable!] (restricted)
    Other versions:
  20. Wayne E. Ferson & Sergei Sarkissian & Timothy T. Simin, 2003. "Spurious Regressions in Financial Economics?," Journal of Finance, American Finance Association, vol. 58(4), pages 1393-1414, 08. [Downloadable!] (restricted)
  21. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 459-491, December. [Downloadable!] (restricted)
    Other versions:
  22. Wayne E. Ferson & Sergei Sarkissian & Timothy Simin, 2002. "Spurious Regressions in Financial Economics?," NBER Working Papers 9143, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  23. Shively, Philip A, 2000. "Stationary Components in Stock Prices: An Exact Pointwise Most Powerful Invariant Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 489-96, October.
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