Quantile Correlations and Quantile Autoregressive Modeling

Li, Guodong; Li, Yang; Tsai, Chih‐Ling

doi:10.1080/01621459.2014.892007

Cited by 131 publications

(57 citation statements)

References 52 publications

(53 reference statements)

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“…where σ 2 a,τ = var.|" t,τ |/ = E[|" t,τ | − μ a,τ ] 2 , with μ a,τ = E|" t,τ |; see also the QACF in Li et al (2015) and the absolute residual ACF in Li and Li (2005). If Q τ .x t |F t−1 / is correctly specified by model (1.2), then E[ψ τ ."…”

Section: Diagnostic Checking For Conditional Quantilesmentioning

confidence: 99%

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Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

Zheng

Zhu

et al. 2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Estimating conditional quantiles of financial time series is essential for risk management and many other financial applications. For time series models with conditional heteroscedasticity, although it is the generalized auto‐regressive conditional heteroscedastic (GARCH) model that has the greatest popularity, quantile regression for this model usually gives rise to non‐smooth non‐convex optimization which may hinder its practical feasibility. The paper proposes an easy‐to‐implement hybrid quantile regression estimation procedure for the GARCH model, where we overcome the intractability due to the square‐root form of the conditional quantile function by a simple transformation. The method takes advantage of the efficiency of the GARCH model in modelling the volatility globally as well as the flexibility of quantile regression in fitting quantiles at a specific level. The asymptotic distribution of the estimator is derived and is approximated by a novel mixed bootstrapping procedure. A portmanteau test is further constructed to check the adequacy of fitted conditional quantiles. The finite sample performance of the method is examined by simulation studies, and its advantages over existing methods are illustrated by an empirical application to value‐at‐risk forecasting.

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Section: Diagnostic Checking For Conditional Quantilesmentioning

confidence: 99%

“…As a result, the computation time is reduced significantly. Furthermore, we construct a portmanteau test to check the adequacy of fitted conditional quantiles based on the residual quantile auto-correlation function (QACF) in Li et al (2015).…”

Section: Introductionmentioning

confidence: 99%

Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

Zheng

Zhu

et al. 2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Furthermore, recent studies have begun to develop properties specifically for QAR models, such as the notion of the quantile correlation (QACF) and quantile partial correlation (QPACF), defined in Li et al [2015] according to the natural quantile extension from standard time series settings for the quantile autocovariance and autocorrelations:…”

Section: Developments Of Quantile Time Series Modelsmentioning

confidence: 99%

General Quantile Time Series Regressions for Applications in Population Demographics

Peters¹

2018

Preprint

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This paper has three objectives, the first is to present a detailed overview in the form of a tutorial for the developments of several key quantile time series modelling approaches. The second objective is to develop a general framework to represent such quantile models in a unifying manner in order to easily develop extensions and connections between existing models that can then be developed to further extend these models in practice. 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 and then to explore each of these core components in detail. The paper is not addressing the concerns of estimation of these models, as there is existing literature on these aspects in many settings, we provide references to relevant works on these aspects in several classes of model. Instead, the focus is rather to provide a unified framework to construct such models for practitioners, therefore the focus is instead on the properties of the models and links between such models from a constructive perspective. 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 based time series data sets of relevance to life insurance analysis. The exploration included detailed mortality, fertility, births and morbidity data in several countries with more detailed analysis of regional data in England, Wales and Scotland.

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“…This draws upon notable work in quantile regression modelling by Koenker [22], [23], [25]; Koenker & Bassett [20]; Gilchrist [13]; and Buchinsky [7], and in the development of quantile time series autoregression models by Koenker & Xiao [24]; Li & Wang [28]; Koenker & Zhao [21]; Lee & Noh [26]; and Aue et al [2]. The development of QAR model properties such as quantile correlation and quantile partial correlation is given by Li et al [27]. Illustrative examples that make a general mapping from a time series model to a quantile times series model through some quantile preserving map are also given in the tutorial.…”

Section: Introductionmentioning

confidence: 96%