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

Author

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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.

Suggested Citation

  • Hashimzade, Nigar & Vogelsang, Timothy, 2006. "Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators," Working Papers 06-04, Cornell University, Center for Analytic Economics.
    • Handle: RePEc:ecl:corcae:06-04
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    References listed on IDEAS

    as
    1. Serena Ng & Pierre Perron, 1996. "The Exact Error In Estimating The Spectral Density At The Origin," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 379-408, July.
    2. Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
    3. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    4. Sun, Yixiao X & Phillips, Peter C. B. & Jin, Sainan, 2005. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing∗," University of California at San Diego, Economics Working Paper Series qt16b3j2hd, Department of Economics, UC San Diego.
    5. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
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    Cited by:

    1. 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.
    2. Bartalotti Otávio, 2019. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-26, January.
    3. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    4. Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 125-147, February.
    5. McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.
    6. 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.
    7. 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.
    8. Vogelsang, Timothy J. & Wagner, Martin, 2014. "Integrated modified OLS estimation and fixed-b inference for cointegrating regressions," Journal of Econometrics, Elsevier, vol. 178(2), pages 741-760.
    9. Otávio 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.
    10. Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    11. Sun, Yu & Yan, Karen X., 2019. "Inference on Difference-in-Differences average treatment effects: A fixed-b approach," Journal of Econometrics, Elsevier, vol. 211(2), pages 560-588.
    12. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
    13. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    14. Cheol-Keun Cho & Timothy J. Vogelsang, 2016. "Fixed- b Inference for Testing Structural Change in a Time Series Regression," Econometrics, MDPI, vol. 5(1), pages 1-26, December.
    15. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
    16. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
    17. Manuel Landajo & María José Presno, 2010. "Stationarity testing under nonlinear models. Some asymptotic results," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 392-405, September.
    18. Vogelsang, Timothy J. & Wagner, Martin, 2013. "A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS," Econometric Theory, Cambridge University Press, vol. 29(3), pages 609-628, June.
    19. 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.
    20. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    21. Yang, Jingjing & Vogelsang, Timothy J., 2018. "Finite sample performance of a long run variance estimator based on exactly (almost) unbiased autocovariance estimators," Economics Letters, Elsevier, vol. 165(C), pages 21-27.
    22. Rhys M. Bidder & Ian Dew-Becker, 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.
    23. Amsler Christine & Schmidt Peter & Vogelsang Timothy J, 2009. "The KPSS Test Using Fixed-b Critical Values: Size and Power in Highly Autocorrelated Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-44, December.

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