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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.

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  • 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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    1. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 857-880.
    2. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 797-814.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
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    1. 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.
    2. Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.
    3. 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.
    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. 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.
    6. Alessandro Casini & Taosong Deng & Pierre Perron, 2021. "Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference," Papers 2103.01604, arXiv.org, revised Nov 2021.
    7. 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.
    8. 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.
    9. 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.

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