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Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation

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  • Phillips, Peter C.B.
  • Sun, Yixiao
  • Jin, Sainan

Abstract

In this paper, we construct a new class of kernel by exponentiating conventional kernels and use them in the long run variance estimation with and without smoothing. Depending on whether the exponent is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimator. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sampling distributions of the spectral density estimator and the associated test statistic in regression settings.

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Bibliographic Info

Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt6mf9q2rt.

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Date of creation: 01 Nov 2004
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Handle: RePEc:cdl:ucsdec:qt6mf9q2rt

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Keywords: Exponentiated Kernel; Lag Kernel; Long Run Variance; Optimal Exponent; Spectral Window; Spectrum;

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Cited by:
  1. Sun, Yixiao & Phillips, Peter C.B. & Jin, Sainan, 2011. "Power Maximization And Size Control In Heteroskedasticity And Autocorrelation Robust Tests With Exponentiated Kernels," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1320-1368, December.
  2. Guay, Alain & Guerre, Emmanuel & Lazarová, Štěpána, 2013. "Robust adaptive rate-optimal testing for the white noise hypothesis," Journal of Econometrics, Elsevier, vol. 176(2), pages 134-145.
  3. Pesaran, M. Hashem & Timmermann, Allan, 2009. "Testing Dependence Among Serially Correlated Multicategory Variables," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 325-337.
  4. Sun, Yixiao, 2013. "Fixed-smoothing Asymptotics in a Two-step GMM Framework," University of California at San Diego, Economics Working Paper Series qt64x4z265, Department of Economics, UC San Diego.
  5. Ray, Surajit & Savin, N.E. & Tiwari, Ashish, 2009. "Testing the CAPM revisited," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 721-733, December.
  6. Wei-Ming Lee & Chung-Ming Kuan, 2006. "Testing Over-Identifying Restrictions without Consistent Estimation of the Asymptotic Covariance Matrix," IEAS Working Paper : academic research 06-A009, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  7. Elmar Mertens, 2008. "Are Spectral Estimators Useful for Implementing Long-Run Restrictions in SVARs?," Working Papers 08.01, Swiss National Bank, Study Center Gerzensee.
  8. Shin-Kun Peng & Takatoshi Tabuchi, 2006. "Spatial Competition in Variety and Number of Stores," IEAS Working Paper : academic research 06-A002, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  9. Yang, Lixiong & Lee, Chingnun & Shie, Fu Shuen, 2014. "How close a relationship does a capital market have with other markets? A reexamination based on the equal variance test," Pacific-Basin Finance Journal, Elsevier, vol. 26(C), pages 198-226.
  10. Preinerstorfer, David & Pötscher, Benedikt M., 2013. "On Size and Power of Heteroscedasticity and Autocorrelation Robust Tests," MPRA Paper 45675, University Library of Munich, Germany.
  11. McElroy, Tucker & Politis, Dimitris, 2013. "Spectral Density and Spectral Distribution Inference for Long Memory Time Series via Fixed-b Asymptotics," University of California at San Diego, Economics Working Paper Series qt6164c110, Department of Economics, UC San Diego.
  12. Steigerwald, Douglas G & Erb, Jack, 2007. "Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity," University of California at Santa Barbara, Economics Working Paper Series qt5rv0z5dz, Department of Economics, UC Santa Barbara.
  13. Mertens, Elmar, 2012. "Are spectral estimators useful for long-run restrictions in SVARs?," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1831-1844.
  14. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
  15. Surajit Ray & N. E. Savin, 2008. "The performance of heteroskedasticity and autocorrelation robust tests: a Monte Carlo study with an application to the three-factor Fama-French asset-pricing model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 91-109.
  16. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.

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