• Bernoulli
  • Volume 24, Number 4A (2018), 2991-3012.

Simultaneous quantile inference for non-stationary long-memory time series

Weichi Wu and Zhou Zhou

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We consider the simultaneous or functional inference of time-varying quantile curves for a class of non-stationary long-memory time series. New uniform Bahadur representations and Gaussian approximation schemes are established for a broad class of non-stationary long-memory linear processes. Furthermore, an asymptotic distribution theory is developed for the maxima of a class of non-stationary long-memory Gaussian processes. Using the latter theoretical results, simultaneous confidence bands for the aforementioned quantile curves with asymptotically correct coverage probabilities are constructed.

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Bernoulli, Volume 24, Number 4A (2018), 2991-3012.

Received: April 2016
Revised: April 2017
First available in Project Euclid: 26 March 2018

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Zentralblatt MATH identifier

heterogeneity local linear quantile estimation long memory simultaneous confidence bands


Wu, Weichi; Zhou, Zhou. Simultaneous quantile inference for non-stationary long-memory time series. Bernoulli 24 (2018), no. 4A, 2991--3012. doi:10.3150/17-BEJ951.

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Supplemental materials

  • Supplement to “Simultaneous quantile inference for non-stationary long-memory time series”. In the supplementary material, we provide complete proofs for lemmas, corollaries, propositions and theorems.