Quantile Periodograms

Li, Ta‐Hsin

doi:10.1080/01621459.2012.682815

Cited by 49 publications

(74 citation statements)

References 12 publications

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“…the joint distribution of (X t , X t+l ), thus allowing to account for sophisticated serial features that simple autocovariances are unable to detect. A detailed discussion on the advantages of the QAF and its representations in the frequency domain (quantile periodogram and quantile spectral density) compared to their respective classical counterparts can be seen in recent references by Lee and Rao (2012), Hagemann (2013), Li (2014) and Dette et al (2014). These works show the usefulness of the quantile versions in specific inference problems like testing for pairwise independence or for equality of serial dependence, and also modeling time series with time-dependent variance.…”

Section: Introductionmentioning

confidence: 96%

Clustering of time series using quantile autocovariances

Lafuente-Rego

Vilar

2015

Adv Data Anal Classif

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Time series clustering is an active research topic with applications in many fields. Unlike conventional clustering on multivariate data, time series often change over time so that the similarity concept between objects must take into account the dynamic of the series. In this paper, a distance measure aimed to compare quantile autocovariance functions is proposed to perform clustering of time series. Quantile autocovariances provide information about the serial dependence structure at different pairs of quantile levels, require no moment condition and allow to identify dependence features that covariance-based methods are unable to detect. Results from an extensive simulation study show that the proposed metric outperforms or is highly competitive with a range of dissimilarities reported in the literature, particularly exhibiting high capability to cluster time series generated from a broad range of dependence models. Estimation of the optimal number of clusters is also addressed. For illustrative purposes, our methodology is applied to a real dataset involving financial time series.

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Section: Introductionmentioning

confidence: 96%

Clustering of time series using quantile autocovariances

Lafuente-Rego

Vilar

2015

Adv Data Anal Classif

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“…Li 2008Li , 2012Li , 2013Li , 2014Hagemann 2013;Lee and Rao 2012;Kley 2014;Dette et al 2015;Kley et al 2016).…”

Section: Laplace and Copula Cumulants And Their Spectral Representationunclassified

“…Further discussion of copula spectra can, for example, be found in Li (2008);Hagemann (2013);Li (2012); Dette et al (2015); Kley et al (2016);Birr, Volgushev, Kley, Dette, and Hallin (2014).…”

Section: Analysis Of the Sandp 500 Stock Index 2007-2010mentioning

confidence: 99%

“…This allows to disentangle the serial features from the marginal features. For a full list of the properties and advantages of these dependence measures the interested reader is referred to Hong (2000); Li (2008Li ( , 2012Li ( , 2013Li ( , 2014; Hagemann (2013); Lee and Rao (2012); Kley (2014); Dette, Hallin, Kley, and Volgushev (2015) and Kley, Volgushev, Dette, and Hallin (2016).…”

Section: Laplace and Copula Cumulants And Their Spectral Representationmentioning

confidence: 99%

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Quantile-Based Spectral Analysis in an Object-Oriented Framework and a Reference Implementation inR: ThequantspecPackage

Kley¹

2016

J. Stat. Soft.

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Quantile-based approaches to the spectral analysis of time series have recently attracted a lot of attention. Several methods for estimation have been proposed in the literature and their statistical properties were analyzed. Yet, so far, neither a systematic method for computation nor a comprehensive software implementation are available to date. This paper contains two main contributions. First, an extensible framework for quantile-based spectral analysis of time series is developed and documented using object-oriented models. A comprehensive, open source reference implementation of this framework is provided in the R package quantspec, which is available from the Comprehensive R Archive Network. The second contribution of the present paper is to provide a detailed tutorial, with worked examples, for this R package. A reader who is already familiar with quantile-based spectral analysis and whose primary interest is not the design of the quantspec package, but how to use it, can read the tutorial and worked examples (Sections 3 and 4) independently.

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“…Koenker and Bassett (1982) rst investigated the case of heteroscedasticity based on regression quantiles, other authors discussed this case for the most prominent quantile, the median (see for example Knight, 1999, Zhao, 2001, and the literature cited there). Quantile regression models for (weakly) dependent data have been studied for LAD estimation by Phillips (1991) and Weiss (1991), for unconditional quantiles in a parametric context by Oberhofer and Haupt (2005), for marginal sample quantiles by Dominicy et al (2012), as an alternative for classical periodogram estimators by Li (2012), for linear regression models by Portnoy (1991) and Fitzenberger (1997). The latter also provides an extensive discussion of bootstrap-based consistent covariance estimation.…”

Section: Introductionmentioning

confidence: 99%