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Robust Nonstationary Regression

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  • Phillips, Peter C.B.

Abstract

This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed which allow for endogeneities in the nonstationary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estimators involve semiparametric corrections to accommodate these possibilities and they belong to the same family as the fully modified least squares (FM-OLS) estimator of Phillips and Hansen (1990). Specific attention is given to fully modified least absolute deviation (FM-LAD) estimation and fully modified M (FM-M)-estimation. The criterion function for LAD and some M-estimators is not always smooth and the paper develops generalized function methods to cope with this difficulty in the asymptotics. The results given here include a strong law of large numbers and some weak convergence theory for partial sums of generalized functions of random variables. The limit distribution theory for FM-LAD and FM-M estimators that is developed includes the case of finite variance errors and the case of heavy-tailed (infinite variance) errors. Some simulations and a brief empirical illustration are reported.

(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): 11 (1995)
Issue (Month): 05 (October)
Pages: 912-951

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Handle: RePEc:cup:etheor:v:11:y:1995:i:05:p:912-951_00

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References

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  1. 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.
  2. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  3. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  4. Peter C.B. Phillips, 1987. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations," Cowles Foundation Discussion Papers 846, Cowles Foundation for Research in Economics, Yale University.
  5. Knight, Keith, 1991. "Limit Theory for M-Estimates in an Integrated Infinite Variance," Econometric Theory, Cambridge University Press, vol. 7(02), pages 200-212, June.
  6. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824, October.
  7. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
  8. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(04), pages 450-463, December.
  9. 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.
  10. repec:cup:etheor:v:7:y:1991:i:4:p:450-63 is not listed on IDEAS
  11. 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.
  12. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  13. Paulauskas, V. J., 1976. "Some remarks on multivariate stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 6(3), pages 356-368, September.
  14. Hunter, John, 1992. "Tests of cointegrating exogeneity for PPP and uncovered interest rate parity in the United Kingdom," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 453-463, August.
  15. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  16. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  17. Resnick, Sidney & Greenwood, Priscilla, 1979. "A bivariate stable characterization and domains of attraction," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 206-221, June.
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Citations

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Cited by:
  1. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October.
  2. 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..
  3. Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2004. "Testing forward exchange rate unbiasedness efficiently: a semiparametric approach," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 325-353, November.
  4. 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.
  5. Michael T. K. Horvath & Mark W. Watson, 1994. "Testing for Cointegration When Some of the Contributing Vectors are Known," NBER Technical Working Papers 0171, National Bureau of Economic Research, Inc.
  6. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(03), pages 696-725, June.
  7. Serguei Zernov & Victoria Zindle-Walsh & John Galbraith, 2006. "Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions," Departmental Working Papers 2006-16, McGill University, Department of Economics.
  8. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
  9. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 215-251, October.
  10. John W. Galbraith & Victoria Zinde-Walsh, 2000. "Properties of Estimates of Daily GARCH Parameters Based on Intra-Day Observations," Econometric Society World Congress 2000 Contributed Papers 1800, Econometric Society.
  11. Xiao, Zhijie, 2004. "Estimating average economic growth in time series data with persistency," Journal of Macroeconomics, Elsevier, vol. 26(4), pages 699-724, December.
  12. Bruno Bosco & Lucia Parisio & Matteo Pelagatti & Fabio Baldi, 2010. "Long-run relations in european electricity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(5), pages 805-832.
  13. Ted Juhl & Zhijie Xiao, 2000. "N-Consistent Semiparametric Regression: Partially Linear Models with Unit Roots," Econometric Society World Congress 2000 Contributed Papers 1532, Econometric Society.
  14. Peter C.B. Phillips, 1994. "Nonstationary Time Series and Cointegration: Recent Books and Themes for the Future," Cowles Foundation Discussion Papers 1081, Cowles Foundation for Research in Economics, Yale University.
  15. Shin, Dong Wan & Oh, Man-Suk, 2004. "Fully modified semiparametric GLS estimation for regressions with nonstationary seasonal regressors," Journal of Econometrics, Elsevier, vol. 122(2), pages 247-280, October.
  16. Victoria Zinde-Walsh, 2009. "Errors-In-Variables Models: A Generalized Functions Approach," Departmental Working Papers 2009-09, McGill University, Department of Economics.
  17. Hodgson, Douglas J., 1998. "Adaptive estimation of cointegrating regressions with ARMA errors," Journal of Econometrics, Elsevier, vol. 85(2), pages 231-267, August.
  18. Caner, Mehmet, 1998. "Tests for cointegration with infinite variance errors," Journal of Econometrics, Elsevier, vol. 86(1), pages 155-175, June.
  19. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.

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