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Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators

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  • Hashimzade, Nigar

    (U of Exeter)

  • Vogelsang, Timothy

    (Cornell U)

Abstract

We propose a new asymptotic approximation for the sampling behavior of nonparametric estimates of the spectral density of a covariance stationary time series. According to the standard approach, the truncation lag grows slower than the sample size. We derive first order limiting distributions under the alternative assumption that the truncation lag is a fixed proportion of the sample size. Our results extend the approach of Neave (1970) who derived a formula for the asymptotic variance of spectral density estimators under the same truncation lag assumption. We show that the limiting distribution of zero frequency spectral density estimators depends on how the data is demeaned. The implications of our zero frequency results are qualitatively similar to exact results for bias and variance computed by Ng and Perron (1996). Finite sample simulations indicate that new asymptotics provides a better approximation than the standard asymptotics when the bandwidth is not small.

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Bibliographic Info

Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 06-04.

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Date of creation: Jan 2006
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Handle: RePEc:ecl:corcae:06-04

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  1. Helle Bunzel & Timothy Vogelsang, 2003. "Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis," Econometrics 0304002, EconWPA.
  2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
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Cited by:
  1. Ai Deng & Pierre Perron, 2005. "A Non-local Perspective on the Power Properties of the CUSUM and CUSUM of Squares Tests for Structural Change," Boston University - Department of Economics - Working Papers Series WP2005-047, Boston University - Department of Economics.
  2. Vogelsang, Timothy J. & Wagner, Martin, 2011. "Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions," Economics Series 263, Institute for Advanced Studies.
  3. Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(1), pages 125-147, February.
  4. Vogelsang, Timothy J. & Wagner, Martin, 2013. "A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS," Econometric Theory, Cambridge University Press, vol. 29(03), pages 609-628, June.
  5. Vogelsang, Timothy J., 2012. "Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects," Journal of Econometrics, Elsevier, vol. 166(2), pages 303-319.
  6. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
  7. Pierre Perron & Tomoyoshi Yabu, 2005. "Estimating Deterministric Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-037, Boston University - Department of Economics.
  8. 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.
  9. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
  10. Ot�vio Bartalotti, 2013. "Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach," Working Papers 1302, Tulane University, Department of Economics, revised Nov 2013.
  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. Bidder, Rhys & Dew-Becker, Ian, 2014. "Long-run risk is the worst-case scenario: ambiguity aversion and non-parametric estimation of the endowment process," Working Paper Series 2014-16, Federal Reserve Bank of San Francisco.
  13. 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.
  14. Sun, Yixiao & Kaplan, David M., 2011. "A New Asymptotic Theory for Vector Autoregressive Long-run Variance Estimation and Autocorrelation Robust Testing," University of California at San Diego, Economics Working Paper Series qt8cx0t4gc, Department of Economics, UC San Diego.

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