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Nonparametric Predictive Regression

  • Ioannis Kasparis
  • Elena Andreou
  • Peter C. B. Phillips

A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The test statistics are related to those of Kasparis and Phillips (2012) and are obtained by kernel regression. The limit distribution of these predictive tests holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. In this sense the proposed tests provide a unifying framework for predictive inference, allowing for possibly nonlinear relationships of unknown form, and offering robustness to integration order and functional form. Under the null of no predictability the limit distributions of the tests involve functionals of independent ÷² variates. The tests are consistent and divergence rates are faster when the predictor is stationary. Asymptotic theory and simulations show that the proposed tests are more powerful than existing parametric predictability tests when deviations from unity are large or the predictive regression is nonlinear. Some empirical illustrations to monthly SP500 stock returns data are provided.

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Paper provided by University of Cyprus Department of Economics in its series University of Cyprus Working Papers in Economics with number 14-2012.

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Length: 49 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:ucy:cypeua:14-2012
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  6. 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.
  7. Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
  8. Lanne, M., 2000. "Testing the Predictability of Stock Returns," University of Helsinki, Department of Economics 488, Department of Economics.
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  15. Peter C.B.Phillips & Ioannis Kasparis, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," Working Papers CoFie-01-2009, Sim Kee Boon Institute for Financial Economics.
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  23. Marmer, Vadim, 2009. "Nonlinearity, Nonstationarity, and Spurious Forecasts," working papers vadim_marmer-2009-60, Vancouver School of Economics, revised 03 Nov 2009.
  24. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
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