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November 2018 Simultaneous quantile inference for non-stationary long-memory time series
Weichi Wu, Zhou Zhou
Bernoulli 24(4A): 2991-3012 (November 2018). DOI: 10.3150/17-BEJ951


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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Weichi Wu. Zhou Zhou. "Simultaneous quantile inference for non-stationary long-memory time series." Bernoulli 24 (4A) 2991 - 3012, November 2018.


Received: 1 April 2016; Revised: 1 April 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853271
MathSciNet: MR3779708
Digital Object Identifier: 10.3150/17-BEJ951

Keywords: Heterogeneity , local linear quantile estimation , long memory , simultaneous confidence bands

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability


Vol.24 • No. 4A • November 2018
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