Piecewise quantile autoregressive modeling for nonstationary time series

Aue, Alexander; Cheung, Rex C. Y.; Lee, Thomas C.; Zhong, Ming

doi:10.3150/14-bej671

Cited by 11 publications

(9 citation statements)

References 21 publications

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“…for taut string estimation. Finally, Aue et al (2014Aue et al ( , 2017 consider quantile segmentation in a time series context based on a minimum description length criterion to select the number of segments and show consistency of their method, whereas in our (simpler) setting we obtain exponentially fast selection consistency, see ( 12).…”

Section: Related Workmentioning

confidence: 96%

Multiscale quantile segmentation

Vanegas¹,

Behr²,

Munk³

2019

Preprint

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We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial independence. It is based on a multiscale statistic, which allows to control the (finite sample) probability for selecting the correct number of segments S at a given error level, which serves as a tuning parameter. For a proper choice of this parameter, this tends exponentially fast to the true S, as sample size increases. We further show that the location and size of segments are estimated at minimax optimal rate (compared to a Gaussian setting) up to a log-factor. Thereby, our approach leads to (asymptotically) uniform confidence bands for the entire quantile regression function in a fully nonparametric setup. The procedure is efficiently implemented using dynamic programming techniques with double heap structures, and software is provided. Simulations and data examples from genetic sequencing and ion channel recordings confirm the robustness of the proposed procedure, which at the same hand reliably detects changes in quantiles from arbitrary distributions with precise statistical guarantees.

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Section: Related Workmentioning

confidence: 96%

Multiscale quantile segmentation

Vanegas¹,

Behr²,

Munk³

2019

Preprint

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“…The second is based on implementing a structural break test to determine the locations of the change-points in the time series, then we can perform what we call segmented quantile regression-based seasonal adjustment. Actually, the concept of the piecewise quantile regression approach has been implemented in different studies (Aue et al (2017); Lahiani (2019); Chen et al (2017)). We evaluate the proposed approaches using simulations of different data generating processes, considering the presence of both the seasonal patterns and the structural breaks.…”

Section: Main Contributions Of the Thesismentioning

confidence: 99%

Quantile regression-based seasonal adjustment

Elseidi¹,

Caporin²

2022

IJCEE

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Time series of different nature might be characterised by the presence of deterministic and/or stochastic seasonal patterns. By seasonality, we refer to periodic fluctuations affecting not only the mean but also the shape, the dispersion and in general the density of the variable of interest over time. Using traditional approaches for seasonal adjustment might not be efficient because they do not ensure, for instance, that the adjusted data are free from periodic behaviours in, say, higher-order moments. We introduce a seasonal adjustment method based on quantile regression that is capable of capturing different forms of deterministic and/or stochastic seasonal patterns. Given a variable of interest, by describing its seasonal behaviour over an approximation of the entire conditional distribution, we are capable of removing seasonal patterns affecting the mean and/or the variance, or seasonal patterns varying over quantiles of the conditional distribution. In the first part of this work, we provide a proposed approach to deal with the deterministic seasonal pattern cases. We provide empirical examples based on simulated and real data where we compare our proposal to least-squares approaches. The results are in favour of the proposed approach in case if the seasonal patterns change across quantiles. In the second part of this work, we improve the proposed approach flexibly to account for the essential effect of the structural breaks in the time series. Again, we compare the proposed methods to segmented-least squares and provide several empirical examples based on simulated and real data that are affected by both the structural breaks and seasonal patterns. The results, in case of stochastic periodic behaviour, are in favour of the proposed approaches especially when the seasonal patterns change across quantiles. Dedicated to my family and my supervisor I would like to express my sincere thanks and gratitude to my supervisor and the course coordinator professor Massimiliano Caporin from the core of my heart for his support, wisdom, encouragement and precious advice and guidance throughout this journey of research. I would like to extend my thanks to the previous course coordinators professor Monica Chiogna and professor Nicola Sartori for their help in all administrative aspects of the doctoral study.I also extend my sincere thanks to all the distinguished professors who taught me during the first year of the PhD. Special thanks also go to Patrizia Piacentini for her assistance to me and all my colleagues before and after our arrival in Padova.My sincere thanks and gratitude to my PhD colleagues for the wonderful time we spent together and for the active participation as a team to successfully complete this stage.My sincere thanks and appreciation to the wonderful and great person don Roberto Ravazzolo, director of the Centro Universitario Padovano, for his permanent assistance, and for the outstanding accommodation that he provided me in the residence of the doctoral students.

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“…Variants of non-stationary QAR models have also been explored in Aue et al (2017). This involves developing locally stationary QAR models through piece-wise, local in time constructions,…”

Section: Developments Of Quantile Time Series Modelsmentioning

confidence: 99%

General Quantile Time Series Regressions for Applications in Population Demographics

Peters

2018

Risks

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The paper addresses three objectives: the first is a presentation and overview of some important developments in quantile times series approaches relevant to demographic applications—secondly, development of a general framework to represent quantile regression models in a unifying manner, which can further enhance practical extensions and assist in formation of connections between existing models for practitioners. In this regard, the core theme of the paper is to provide perspectives to a general audience of core components that go into construction of a quantile time series model. The third objective is to compare and discuss the application of the different quantile time series models on several sets of interesting demographic and mortality related time series data sets. This has relevance to life insurance analysis and the resulting exploration undertaken includes applications in mortality, fertility, births and morbidity data for several countries, with a more detailed analysis of regional data in England, Wales and Scotland.

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Piecewise quantile autoregressive modeling for nonstationary time series

Cited by 11 publications

References 21 publications

Multiscale quantile segmentation

Multiscale quantile segmentation

Quantile regression-based seasonal adjustment

General Quantile Time Series Regressions for Applications in Population Demographics

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