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The Local Bootstrap for Periodogram Statistics

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  • Efstathios Paparoditis
  • Dimitris N. Politis

Abstract

A bootstrap procedure for the periodogram of a weakly dependent stationary sequence is proposed. The method works by locally resampling the periodogram ordinates and does not require estimation of the spectral density and of frequency domain residuals obtained by means of initial smoothing. Asymptotic properties of the proposed bootstrap procedure are studied and consistency is proved for interesting classes of statistics including ratio statistics, kernel estimates of the spectral density and parameter estimates. Some practical aspects concerning the implementation of the method are also discussed.

Suggested Citation

  • Efstathios Paparoditis & Dimitris N. Politis, 1999. "The Local Bootstrap for Periodogram Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(2), pages 193-222, March.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:2:p:193-222
    DOI: 10.1111/1467-9892.00133
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    Citations

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    Cited by:

    1. Arteche, Josu & Orbe, Jesus, 2016. "A bootstrap approximation for the distribution of the Local Whittle estimator," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 645-660.
    2. Jentsch, Carsten & Kreiss, Jens-Peter, 2010. "The multiple hybrid bootstrap -- Resampling multivariate linear processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2320-2345, November.
    3. Arteche, Josu & Orbe, Jesus, 2017. "A strategy for optimal bandwidth selection in Local Whittle estimation," Econometrics and Statistics, Elsevier, vol. 4(C), pages 3-17.
    4. Arteche González, Jesús María, 2020. "Frequency Domain Local Bootstrap in long memory time series," BILTOKI info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    5. Arteche González, Jesús María & Orbe Lizundia, Jesús María, 2008. "Selection of the number of frequencies using bootstrap techniques in log-periodogram regression," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    6. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
    7. Dimitris Politis, 2013. "Rejoinder on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 240-250, June.
    8. Ta‐Hsin Li, 2021. "Quantile‐frequency analysis and spectral measures for diagnostic checks of time series with nonlinear dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 270-290, March.
    9. Arteche, Josu, 2024. "Bootstrapping long memory time series: Application in low frequency estimators," Econometrics and Statistics, Elsevier, vol. 29(C), pages 1-15.
    10. Peter Buhlmann, 2007. "Bootstrap schemes for time series (in Russian)," Quantile, Quantile, issue 3, pages 37-56, September.
    11. J -P Kreiss & E Paparoditis, 2023. "Bootstrapping Whittle estimators," Biometrika, Biometrika Trust, vol. 110(2), pages 499-518.
    12. Franco, Glaura C. & Reisen, Valderio A., 2007. "Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 546-562.
    13. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    14. Silva, E.M. & Franco, G.C. & Reisen, V.A. & Cruz, F.R.B., 2006. "Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1002-1011, November.

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