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

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

Abstract

A new class of kernels for long-run variance and spectral density estimation is developed by exponentiating traditional quadratic kernels. Depending on whether the exponent parameter is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimators. 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 sample distributions of the spectral density estimator and the associated test statistic in regression settings. Copyright 2006 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

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Bibliographic Info

Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 47 (2006)
Issue (Month): 3 (08)
Pages: 837-894

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Handle: RePEc:ier:iecrev:v:47:y:2006:i:3:p:837-894

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Cited by:
  1. Shin-Kun Peng & Takatoshi Tabuchi, 2007. "Spatial Competition in Variety and Number of Stores," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(1), pages 227-250, 03.
  2. Elmar Mertens, 2010. "Are spectral estimators useful for implementing long-run restrictions in SVARs?," Finance and Economics Discussion Series 2010-09, Board of Governors of the Federal Reserve System (U.S.).
  3. Lee, Wei-Ming & Kuan, Chung-Ming & Hsu, Yu-Chin, 2014. "Testing over-identifying restrictions without consistent estimation of the asymptotic covariance matrix," Journal of Econometrics, Elsevier, vol. 181(2), pages 181-193.
  4. 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.
  5. M. Hashem Pesaran & Allan Timmermann, 2006. "Testing Dependence among Serially Correlated Multi-category Variables," CESifo Working Paper Series 1770, CESifo Group Munich.
  6. 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.
  7. 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.
  8. Preinerstorfer, David & Pötscher, Benedikt M., 2013. "On Size and Power of Heteroscedasticity and Autocorrelation Robust Tests," MPRA Paper 45675, University Library of Munich, Germany.
  9. Yixiao Sun & Peter C.B. Phillips & Sainan Jin, 2010. "Power Maximization and Size Control in Heteroskedasticity and Autocorrelation Robust Tests with Exponentiated Kernels," Cowles Foundation Discussion Papers 1749, Cowles Foundation for Research in Economics, Yale University.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Ray, Surajit & Savin, N.E. & Tiwari, Ashish, 2009. "Testing the CAPM revisited," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 721-733, December.

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