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Nonstationary Nonlinear Heteroskedasticity in Regression

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  • Park, Joon

    (Rice University and Sungkyunkwan University)

  • Chung, Heetaik

    (Handong University)

Abstract

This paper considers the regression with errors having nonstationary nonlinear heteroskedasticity. For both the usual stationary regression and the nonstationary cointegrating regression, we develop the asymptotic theories for theleast squares methods in the presence of conditional heterogeneity given as a nonlinear function of an integrated process. The conditional heteroskedasticity generated by an integrated process has more fundamental effects on the regression asymptotics than the one generated by a stationary process. In particular, the nonstationarity of volatility in the regression errors may induce spuriousness of the underlying regression. This is true for both the usual stationary regression and the nonstationary cointegrating regression, if excessive nonstationary volatility is present in the errors. Mild nonstationary volatilities do not render the underlying regression spurious. However, their presence makes the least squares estimator asymptotically biased and inefficient and the usual chi-square test invalid. We provide some illustrations to demonstrate the empirical relevancy of the model and theory developed in the paper. For this purpose, examined are US consumption function, EURO/USD forward-spot spreads and capital-asset pricing models for some major NYSE stocks.

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Bibliographic Info

Paper provided by Rice University, Department of Economics in its series Working Papers with number 2004-02.

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Date of creation: Aug 2005
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Handle: RePEc:ecl:riceco:2004-02

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  1. Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
  2. J. Isaac Miller & Joon Y. Park, 2008. "Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory," Working Papers 0801, Department of Economics, University of Missouri.
  3. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  4. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  6. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. 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.
  9. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
  10. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  11. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
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Cited by:
  1. Han, Heejoon & Park, Joon Y., 2006. "Time series properties of ARCH processes with persistent covariates," MPRA Paper 5199, University Library of Munich, Germany.
  2. Ke-Li Xu & Peter C.B. Phillips, 2006. "Adaptive Estimation of Autoregressive Models with Time-Varying Variances," Cowles Foundation Discussion Papers 1585, Cowles Foundation for Research in Economics, Yale University.
  3. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
  4. Kim, Chang Sik & Kim, In-Moo, 2012. "Partial parametric estimation for nonstationary nonlinear regressions," Journal of Econometrics, Elsevier, vol. 167(2), pages 448-457.
  5. Xu, Ke-Li, 2008. "Testing against nonstationary volatility in time series," Economics Letters, Elsevier, vol. 101(3), pages 288-292, December.

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