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Nonstationary Nonlinear Heteroskedasticity in Regression

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  • Joon Y. Park
  • Heetaik Chung

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 the least squares methods in the presence of conditional heterogeneity given as a nonlinear function of an integrated process. In particular, it is shown that 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. In the paper, we develop an unbiased and efficient method of estimation and a chi-square test applicable for the regression with mild nonstationary volatilities in the errors. 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 Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 508.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:508

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Keywords: volatility; nonstationary nonlinear heteroskedasticity; regression with heteroskedastic errors; spurious regression; cointegration;

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References

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  1. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  5. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
  6. Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
  7. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  8. Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
  9. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  10. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
  11. 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.
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Cited by:
  1. Xu, Ke-Li, 2008. "Testing against nonstationary volatility in time series," Economics Letters, Elsevier, vol. 101(3), pages 288-292, December.
  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. Han, Heejoon & Park, Joon Y., 2008. "Time series properties of ARCH processes with persistent covariates," Journal of Econometrics, Elsevier, vol. 146(2), pages 275-292, October.
  5. Kim, Chang Sik & Kim, In-Moo, 2012. "Partial parametric estimation for nonstationary nonlinear regressions," Journal of Econometrics, Elsevier, vol. 167(2), pages 448-457.

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