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Banded and Tapered Estimates for Autocovariance Matrices and the Linear Process Bootstrap

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  • McMurry, Timothy L
  • Politis, D N

Abstract

We address the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down-weighting o�-diagonal entries towards zero. In addition we show the same convergence rates hold for a positive de�nite version of the estimator, and we introduce a new approach for selecting the banding parameter. The new matrix estimator is shown to perform well theoretically and in simulation studies. As an application we introduce a new resampling scheme for stationary processes termed the linear process bootstrap (LPB). The LPB is shown to be asymptotically valid for the sample mean and related statistics. The e�ectiveness of the proposed methods are demonstrated in a simulation study.

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  • McMurry, Timothy L & Politis, D N, 2010. "Banded and Tapered Estimates for Autocovariance Matrices and the Linear Process Bootstrap," University of California at San Diego, Economics Working Paper Series qt5h9259mb, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt5h9259mb
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    1. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
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    Cited by:

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    6. Tommaso Proietti & Alessandro Giovannelli, 2018. "A Durbin–Levinson regularized estimator of high-dimensional autocovariance matrices," Biometrika, Biometrika Trust, vol. 105(4), pages 783-795.
    7. Timothy L. McMurry & Dimitris N. Politis, 2010. "Banded and tapered estimates for autocovariance matrices and the linear process bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 471-482, November.
    8. Petropoulos, Fotios & Hyndman, Rob J. & Bergmeir, Christoph, 2018. "Exploring the sources of uncertainty: Why does bagging for time series forecasting work?," European Journal of Operational Research, Elsevier, vol. 268(2), pages 545-554.
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    14. Ouyang, Yanyan & Liu, Jiamin & Tong, Tiejun & Xu, Wangli, 2022. "A rank-based high-dimensional test for equality of mean vectors," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
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    16. Konrad Furmańczyk, 2021. "Estimation of autocovariance matrices for high dimensional linear processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 595-613, May.
    17. Dimitris Politis, 2013. "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 183-221, June.
    18. Abadir, Karim M. & Distaso, Walter & Žikeš, Filip, 2014. "Design-free estimation of variance matrices," Journal of Econometrics, Elsevier, vol. 181(2), pages 165-180.
    19. Cheng, Tzu-Chang F. & Ing, Ching-Kang & Yu, Shu-Hui, 2015. "Toward optimal model averaging in regression models with time series errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 321-334.
    20. Holger Dette & Weichi Wu, 2020. "Prediction in locally stationary time series," Papers 2001.00419, arXiv.org, revised Jan 2020.
    21. Ryan Janicki & Tucker S. McElroy, 2016. "Hermite expansion and estimation of monotonic transformations of Gaussian data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 207-234, March.
    22. Politis, Dimitris, 2014. "High-dimensional autocovariance matrices and optimal linear prediction," University of California at San Diego, Economics Working Paper Series qt3k58p0xr, Department of Economics, UC San Diego.
    23. Meira, Erick & Cyrino Oliveira, Fernando Luiz & de Menezes, Lilian M., 2021. "Point and interval forecasting of electricity supply via pruned ensembles," Energy, Elsevier, vol. 232(C).
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    25. Holger Dette & Theresa Eckle & Mathias Vetter, 2020. "Multiscale change point detection for dependent data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1243-1274, December.

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