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Time Series Regression With a Unit Root and Infinite-Variance Errors

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  • Phillips, P.C.B.

Abstract

Chan and Tran give the limit theory for the least squares coefficient in a random walk with the iid errors that are in the domain of attraction of a stable law. This note discusses their results and provides generalizations to the case of I(q) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. General unit root tests are also studied. It is shown that the semiparametric corrections suggested by the author for the finite variance case continue to work when the errors have infinite variance. The limit laws are expressed in terms of ratios of quadratic functionals of a stable process rather than Brownian motion. The correction terms that eliminate nuisance parameter dependencies are random in the limit and involve multiple stochastic integrals that may be written in terms of the quadratic variation of the limiting stable process.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 6 (1990)
Issue (Month): 01 (March)
Pages: 44-62

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Handle: RePEc:cup:etheor:v:6:y:1990:i:01:p:44-62_00

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References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  2. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  3. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  4. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  5. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(03), pages 354-362, December.
  6. Peter C.B. Phillips & Vassilis A. Hajivassiliou, 1987. "Bimodal t-Ratios," Cowles Foundation Discussion Papers 842, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Phillips, Peter C. B. & McFarland, James W., 1997. "Forward exchange market unbiasedness: the case of the Australian dollar since 1984," Journal of International Money and Finance, Elsevier, vol. 16(6), pages 885-907, December.
  2. Marc Sáez & Robert M. Kunst, 1995. "ARCH patterns in cointegrated systems," Economics Working Papers 110, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Shin, Dong Wan & So, Beong Soo, 1999. "New tests for unit roots in autoregressive processes with possibly infinite variance errors," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 387-397, October.
  4. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
  5. So, Beong Soo & Shin, Dong Wan, 2001. "An invariant sign test for random walks based on recursive median adjustment," Journal of Econometrics, Elsevier, vol. 102(2), pages 197-229, June.
  6. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
  7. Phillips, Peter C B & McFarland, James W & McMahon, Patrick C, 1996. "Robust Tests of Forward Exchange Market Efficiency with Empirical Evidence from the 1920s," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 1-22, Jan.-Feb..
  8. Peter C.B. Phillips & Mico Loretan, 1990. "Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns," Cowles Foundation Discussion Papers 947, Cowles Foundation for Research in Economics, Yale University.
  9. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.
  10. Qin, Ruibing & Tian, Zheng & Jin, Hao & Zhang, Xiaowei, 2010. "Strong convergence rate of robust estimator of change point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2026-2032.
  11. Paulo M. M. Rodrigues & Antonio Rubia, 2004. "On the Small Sample Properties of Dickey Fuller and Maximum Likelihood Unit Root Tests on Discrete-Sampled Short-Term Interest Rates," Econometrics 0405004, EconWPA.
  12. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
  13. Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers 8, University of Verona, Department of Economics.
  14. Guglielmo Caporale & Nikitas Pittis, 2001. "Parameter instability, superexogeneity, and the monetary model of the exchange rate," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 137(3), pages 501-524, September.
  15. Miller, J. Isaac & Park, Joon Y., 2005. "How They Interact to Generate Persistency in Memory," Working Papers 2005-01, Rice University, Department of Economics.
  16. Datta, Somnath, 1995. "Limit theory and bootstrap for explosive and partially explosive autoregression," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 285-304, June.
  17. K. D. Patterson & S. M. Heravi, 2003. "The impact of fat-tailed distributions on some leading unit roots tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 635-667.
  18. Caner, Mehmet, 1998. "Tests for cointegration with infinite variance errors," Journal of Econometrics, Elsevier, vol. 86(1), pages 155-175, June.
  19. Mikael Linden, 1992. "Stochastic and deterministic trends in Finnish macroeconomic time series," Finnish Economic Papers, Finnish Economic Association, vol. 5(2), pages 110-116, Autumn.

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