## Fixed-smoothing asymptotics for time series.(English)Zbl 1273.62231

Summary: We derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based $$t$$-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of the asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location models.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62E20 Asymptotic distribution theory in statistics 62G09 Nonparametric statistical resampling methods 62G20 Asymptotic properties of nonparametric inference

### Keywords:

bootstrap; high-order expansions; long-run variance matrix
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### References:

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