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The multiple hybrid bootstrap -- Resampling multivariate linear processes

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  • Jentsch, Carsten
  • Kreiss, Jens-Peter

Abstract

The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested in Kreiss and Paparoditis (2003) [18]. Their idea was to combine a time domain parametric and a frequency domain nonparametric bootstrap to mimic not only a part but as much as possible the complete covariance structure of the underlying time series. We extend the AAPB in two directions. Our procedure explicitly leads to bootstrap observations in the time domain and it is applicable to multivariate linear processes, but agrees exactly with the AAPB in the univariate case, when applied to functionals of the periodogram. The asymptotic theory developed shows validity of the multiple hybrid bootstrap procedure for the sample mean, kernel spectral density estimates and, with less generality, for autocovariances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2320-2345
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    References listed on IDEAS

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    1. 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.
    2. Dahlhaus, Rainer, 1985. "Asymptotic normality of spectral estimates," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 412-431, June.
    3. Efstathios Paparoditis, 2005. "Testing the Fit of a Vector Autoregressive Moving Average Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 543-568, July.
    4. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    5. Ming Dai, 2004. "Multivariate spectral analysis using Cholesky decomposition," Biometrika, Biometrika Trust, vol. 91(3), pages 629-643, September.
    6. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
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    Cited by:

    1. Stefan Bruder & Michael Wolf, 2018. "Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 641-664, September.
    2. Fiecas, Mark & von Sachs, Rainer, 2013. "Data-driven Shrinkage of the Spectral Density Matrix of a High-dimensional Time Series," LIDAM Discussion Papers ISBA 2013044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    4. Franziska Häfner & Claudia Kirch, 2017. "Moving Fourier Analysis for Locally Stationary Processes with the Bootstrap in View," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 895-922, November.
    5. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Haihan Yu & Mark S Kaiser & Daniel J Nordman, 2023. "A subsampling perspective for extending the validity of state-of-the-art bootstraps in the frequency domain," Biometrika, Biometrika Trust, vol. 110(4), pages 1099-1115.
    7. Peter Brockwell & Jens-Peter Kreiss & Tobias Niebuhr, 2014. "Bootstrapping continuous-time autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 75-92, February.
    8. C. Jentsch & J.-P. Kreiss & P. Mantalos & E. Paparoditis, 2012. "Hybrid bootstrap aided unit root testing," Computational Statistics, Springer, vol. 27(4), pages 779-797, December.
    9. Liu, Yixuan & Kirch, Claudia & Lee, Jeong Eun & Meyer, Renate, 2024. "A nonparametrically corrected likelihood for Bayesian spectral analysis of multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).
    10. Fiecas, Mark & von Sachs, Rainer, 2012. "Spectral density shrinkage for high-dimensional time series," LIDAM Discussion Papers ISBA 2012037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Kim, Young Min & Nordman, Daniel J., 2013. "A frequency domain bootstrap for Whittle estimation under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 405-420.

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