Bernoulli

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

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

Abstract

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.

Article information

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

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

https://projecteuclid.org/euclid.bj/1522051231

Digital Object Identifier
doi:10.3150/17-BEJ951

Mathematical Reviews number (MathSciNet)
MR3779708

Zentralblatt MATH identifier
06853271

Citation

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. https://projecteuclid.org/euclid.bj/1522051231

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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.