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    On the validity of resampling methods under long memory

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    Date Issued
    2017-12-01
    Publisher Version
    10.1214/16-AOS1524
    Author(s)
    Bai, Shuyang
    Taqqu, Murad S.
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    Permanent Link
    https://hdl.handle.net/2144/39138
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    Accepted manuscript
    Citation (published version)
    Shuyang Bai, Murad S Taqqu. 2017. "ON THE VALIDITY OF RESAMPLING METHODS UNDER LONG MEMORY." ANNALS OF STATISTICS, Volume 45, Issue 6, pp. 2365 - 2399 (35). https://doi.org/10.1214/16-AOS1524
    Abstract
    For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic consistency of subsampling procedures for general statistics under long memory. It allows the subsample size b to be o(n), where n is the sample size, irrespective of the strength of the memory. We are then able to improve many results found in the literature. We also consider applications of subsampling procedures under long memory to the sample covariance, M-estimation and empirical processes.
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    • CAS: Mathematics & Statistics: Scholarly Papers [280]
    • BU Open Access Articles [3866]


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