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Renewal type bootstrap for increasing degree U-process of a Markov chain. J MULTIVARIATE ANAL 2022. [DOI: 10.1016/j.jmva.2022.105143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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Bai S, Taqqu MS. How the Instability of Ranks Under Long Memory Affects Large-Sample Inference. Stat Sci 2018. [DOI: 10.1214/17-sts633] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Dehling H, Rooch A, Wendler M. Two-sample U-statistic processes for long-range dependent data. STATISTICS-ABINGDON 2017. [DOI: 10.1080/02331888.2016.1270542] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- H. Dehling
- Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
| | - A. Rooch
- Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
| | - M. Wendler
- Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, Germany
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Abstract
For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.
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Abstract
For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.
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Podolskij M, Schmidt C, Ziegel JF. Limit theorems for nondegenerate U-statistics of continuous semimartingales. ANN APPL PROBAB 2014. [DOI: 10.1214/13-aap983] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Beutner E, Zähle H. Continuous mapping approach to the asymptotics of $U$- and $V$-statistics. BERNOULLI 2014. [DOI: 10.3150/13-bej508] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Leucht A, Neumann MH. Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics. ANN I STAT MATH 2012. [DOI: 10.1007/s10463-012-0374-9] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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DEHLING HEROLD, ROOCH AENEAS, TAQQU MURADS. Non-Parametric Change-Point Tests for Long-Range Dependent Data. Scand Stat Theory Appl 2012. [DOI: 10.1111/j.1467-9469.2012.00799.x] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Lévy-Leduc C, Boistard H, Moulines E, Taqqu MS, Reisen VA. Asymptotic properties of U-processes under long-range dependence. Ann Stat 2011. [DOI: 10.1214/10-aos867] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Kulik R. Empirical process of long-range dependent sequences when parameters are estimated. J Stat Plan Inference 2009. [DOI: 10.1016/j.jspi.2008.05.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Haye MO. Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonal long-memory. ESAIM-PROBAB STAT 2002. [DOI: 10.1051/ps:2002016] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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