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The Exact Error In Estimating The Spectral Density At The Origin

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  • Serena Ng
  • Pierre Perron

Abstract

. This paper derives expressions for the exact bias and variance of a general class of spectral density estimators at the zero frequency, building on the work of Neave (The exact error in spectrum estimates. Ann. Math. Statist. 42 (1971), 961–75) who studied the case where the mean of the series is assumed known. These expressions are evaluated for 15 different windows and for a wide variety of stationary time series. The exact error of the estimators is found to depend on whether the sample mean has to be estimated, and some windows are noticeably inferior at certain values of the bandwidth. A response surface analysis reveals that the finite sample relationships between the bandwidth and the exact error are quite different from the ones suggested by asymptotic theory.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:17:y:1996:i:4:p:379-408
    DOI: 10.1111/j.1467-9892.1996.tb00284.x
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    Cited by:

    1. 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.
    2. 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.
    3. Paulo Parente & Richard J. Smith, 2024. "Implied probability kernel block bootstrap for time series moment condition models," CeMMAP working papers 08/24, Institute for Fiscal Studies.
    4. Lijuan Huo & Jin Seo Cho, 2019. "Testing for the Sandwich-Form Covariance Matrix Applied to Quasi-Maximum Likelihood Estimation Using Economic and Energy Price Growth Rates," Working papers 2019rwp-152, Yonsei University, Yonsei Economics Research Institute.
    5. Casini, Alessandro & Deng, Taosong & Perron, Pierre, 2026. "Theory Of Low Frequency Contamination From Nonstationarity And Misspecification: Consequences For Har Inference," Econometric Theory, Cambridge University Press, vol. 42(2), pages 294-335, April.
    6. Paulo M.D.C. Parente & Richard J. Smith, 2018. "Generalised Empirical Likelihood Kernel Block Bootstrapping," Working Papers REM 2018/55, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    7. Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.
    8. Fouquau, Julien & Spieser, Philippe K., 2015. "Statistical evidence about LIBOR manipulation: A “Sherlock Holmes” investigation," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 632-643.
    9. Youngsoo Bae & Robert M. de Jong, 2007. "Money demand function estimation by nonlinear cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 767-793.
    10. Lijuan Huo & Jin Seo Cho, 2021. "Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 293-317, June.
    11. Ali Sami Rashid & Mohammed Jabber Hawas Allami & Ahmed Kareem Mutasher, 2020. "Best Lag Window for Spectrum Estimation of Law Order MA Process," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).

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