A unified approach to self-normalized block sampling
Taqqu, Murad S.
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Citation (published version)Shuyang Bai, Murad S Taqqu, Ting Zhang. 2016. "A unified approach to self-normalized block sampling." STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Volume 126, Issue 8, pp. 2465 - 2493 (29). https://doi.org/10.1016/j.spa.2016.02.007
The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range dependent, or whether it has a light or heavy-tailed marginal distribution. In the current paper, we develop an asymptotic theory for the self-normalized block sampling, and prove that the corresponding block sampling method can provide a unified inference approach for the aforementioned different situations in the sense that it does not require the a priori estimation of auxiliary parameters. Monte Carlo simulations are presented to illustrate its finite-sample performance. The R function implementing the method is available from the authors.