Shortterm power load probability density forecasting method. The properties of the proposed estimator and prediction are established theoreti cally, and assessed numerically through a simulation study and the analysis of a. We propose a highdimensional copula to model the dependence structure of the seemingly unrelated quantile regression. Recent publications lehrstuhl fur mathematische statistik. Even though this technique is driven by copula based quantile regression model, it retains more flexibility and thus, should deliver more robust and accurate estimates. Copula quantile regression and measurement of risk in finance. Introduction arellano and bonhomme 2017 have recently proposed a new approach to analysing sample selection e ects in the context of a general quantile regression. Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in.
Prediction via the quantilecopula conditional density estimator. An r package for dvine copula based mean and quantile regression. Additionally, the copula based approach allows the analyst to spontaneously take account of common regression concerns such as interactions between covariates or possible transformations of the latter. In this work a semiparametric copula based estimator for conditional quantiles is investigated for complete or rightcensored data. Analysis of train derailment severity using vine copula. In contrast to traditional linear quantile regression, no distributional assumptions are made and quantiles for di erent quantile levels cannot cross each other. We introduce a general approach to nonlinear quantile regression modelling based on the copula function that defines the dependency structure between the. Oct 18, 2016 nelsen explained in his 1999 book an introduction to copulas how to fit a nonlinear quantile regression model by means of a bivariate copula pp. The monte carlo simulations show good results of the proposed weighted method. Besides, depending on the choice of the copula function, the relationship between the two random variables can be nonlinear, offering some flexibility in the modeling of the dependence between these two variables. A quantilecopula approach to dependence between financial. Pdf we propose a highdimensional copula to model the dependence structure of the seemingly unrelated quantile regression. We introduce a general approach to nonlinear quantile regression modelling that is based on the specification of the copula function that defines the dependency. Deep generative quantile copula models for probabilistic forecasting ruofeng wen 1kari torkkola abstract we introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation.
This rpackages presents a bivariate, copula based model for the joint distribution of a pair of continuous and discrete random variables. The major interest is the covariate effects on the quantile of the nonterminal event time. The resulting quantile regression estimator has the valuable property of being automatically monotonic across quantile levels. Just as linear regression estimates the conditional mean function as a linear combination of the predictors, quantile regression estimates the conditional quantile function as a linear combination of the predictors. Nonlinearity in quantile regression was developed by powell 1986 using a censored model. For a recent overview of quantile regression see yu, lu,andstander 2001. Quantile regression estimators have the same equivariance property as the ordinary least square ols estimators but the equivariance to monotone transformations is specific only to quantile regression see koenker, 2005 for more details. Copulas are powerful explanatory tools for studying dependence patterns in multivariate data. Thus, after an estimator for t has been obtained, we can estimate,kt using one of the existing techniques for a simple varyingcoe. This library provides functions for dvine copula based mean and quantile regression.
Moreover,bouy e and salmon2009 propose a general approach to nonlinear quantile regression with one predictor based on a copula function. This paper proposes a weighted quantile regression method on high quantile regression for certain extreme value sets. Bayesian estimation of archimedean copulabased sur. The two marginal random variables are modeled via generalized linear models, and their joint distribution represented by a parametric copula family is estimated using maximumlikelihood techniques.
Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial applications. Dependent censoring is handled by assuming that the joint distribution of the two event times follows a parametric copula model with. The power load forecast accuracy are assessed by three cases of singapore. Oct 14, 2008 in this paper we use the archimedean copula nonlinear conditional quantile regression model to measure the tail area risk dependence in shanghai and shenzhen stock markets with 600 groups of data of daily closing prices from january 4, 2005 to august 21, 2007. While the primary use of copula models is in multivariate dependence modelling, they also offer predictive value for regression analysis. The other factors are fixed at values specified on the pane options dialog box. Regression quantiles, as introduced in a seminal work by koenker and bassett 1978, remain a lively area of research with several recent advances. Nov 19, 2015 the quantile regression tool is employed to specify the entire conditional distribution of downscaled variables and to address the limitations of traditional regression based approaches whereas the gaussian copula is performed to describe and preserve the dependence between both variables and sites. Specification of, say, the copula function may be investigated based on parameter constancy over quantiles, along the lines of koenker and xiao 2006. The findings provide greater comprehension of the influence of the covariates on train derailment severity. The paper proposes a shortterm power load probability density forecasting method using kernelbased support vector quantile regression ksvqr and copula theory.
The authors introduce a new semiparametric quantile regression method based on sequentially fitting a likelihood optimal dvine copula to given data resulting in highly. Through numerical studies, section 3 describes predictionbased copula model selection criteria and evaluates the predictive discrepancy between bivariate copula models, as well as the linear regression model. Multisite and multivariable statistical downscaling using. Introduction arellano and bonhomme 2017 have recently proposed a new approach to analysing sample selection e ects in the context of a general quantile regression model, thereby ex. Feb 02, 2021 dvine copula based quantile regression. Request pdf dvine copula based quantile regression quantile regression, that is the prediction of a random variables quantiles conditioned on other random variables taking on certain values. Pdf dynamic copula quantile regressions and tail area. Deep generative quantilecopula models for probabilistic. Multisite and multivariable statistical downscaling using a. I propose the copula quantileonquantile regression cqqr approach to construct the correlation between the conditional quantiles of stock returns. Gaussian copula regression in r civil, environmental and.
In short, nelsens method for fitting a nonlinear quantile regression model is as follows. As a subclass of regular vine copulas, dvines enable the modeling of multivariate copulas in. With the application of stress testing, a task with increasing relevance in the nancial world, we show how dvine copula based quantile regression can be. Conditional quantile function, copula, quantile regression. This paper considers quantile regression analysis based on semicompeting risks data in which a nonterminal event may be dependently censored by a terminal event. See lee 1983, smith 2003, or the recent application in van kerm 20 for example.
Actually, our proposal is an extension of the recent work of noh et al. The secondary objective of this paper is to investigate the nonlinear relationships among variables through the use of two different archimedean copulas with. Undermodelconditions, quantile residuals r i are, approximately, realizations of uncorrelated standard normal variables and they are unrelated to the covariates x i. A co pulabased quant ileonquantile regression approa ch to. Semiparametric copula quantile regression for complete or. Quantile regression uses an l1 loss function, and the optimal solution of linear programming for estimating coefficients of regression. Quantile regression analysis has received increasing at tentions in the recent literature of survival analysis. In addition, specification of conditional quantile models can be. Dvine copula based quantile regression request pdf. The vine copula quantile regression model was found to offer better accuracy for analyzing derailment severity at various confidence levels compared to the classical quantile regression approach. The main purpose of dvine copula based quantile regression is to predict the quantile of the response variable y according to the auxiliary variables x 1.
Koenker 2004 extends the quantile regression to panel data applications and introduces a general approach to estimating quantile regression models for longitudinal data. A copula based quantile regression approach jongmin kim 1, chanho cho 2, chulhee jun 3 and won yong kim 4, 1 statistics discipline, division of science and mathematics, university of minnesotamorris, morris, mn 56267, usa. Quantile regression is a regression method for estimating these conditional quantile functions. In spirit, the methodology is extending the recent work of noh et al. As the kernel function can influence the prediction performance, three kernel functions are compared in. Quantile regression based on semicompeting risks data. Krenar avdulaj and jozef barunik a semiparametric nonlinear. Seemingly unrelated quantile regression under asymmetric laplace distribution. This approach obviously relies heavily on the correct speci. R code for performing quantile regression using bivariate. Copula regression spline models for binary outcomes. They also gave the simple closed forms of 1 the example of clayton copula with its quantile function is given in next subsection. Dvine copula based quantile regression sciencedirect.
Testing conditional independence via quantile regression. With the application of stress testing, a task with increasing relevance in the nancial world, we show how dvine copula based quantile regression can be used in practice. Packageslibraries lehrstuhl fur mathematische statistik. The proposed svqr can implement power load probability density forecasting. Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial. Journal of risk and financial management article the changing dynamics of board independence. A non quantile regression based approach to selection correction is to parametrically specify both outcome and selection equations, thus providing nongaussian extensions to the heckman model. Dvine copula based quantile regression and the simplifying. Jones in the discussion of cole 1988 have suggested that quantile regression methods may o. A co pulabased quant ileonquantile regression approa ch. Quantile regression yields valuable insights in applications such as risk. Copula based seemingly unrelated quantile regression model 2. Quantile regression and extreme value analysis statistical. Pdf recently, two different copula based approaches have been.
Financial econometrics research centre, warwick business school, uk we introduce a general approach to nonlinear quantile regression modelling based on the copula function that defines the. Conditional quantiles and tail dependence sciencedirect. Masarotto and varin2012 suggest to validate gaussian copula regression models for con. Relative to fully parametric approaches, quantile regression provides.
Compared with conventional regression models such as the proportional hazards ph model or the accelerated. In other terms, the parameters of interest are the regression coefficients, while the dependence structure identified by the gaussian copula is a nuisance component. As the conventional model faces with the strong assumption of the multivariate normal distribution and the linear dependence structure, thus, we apply the multivariate exchangeable copula function to relax this assumption. Commonly used methods of estimating var include copula models, arch models. The underlying censoring mechanism is characterized by an archimedean copula for the dependent variable and the censoring variable. Partial identication and inference in censored quantile. This is a scaled version of the squared norm of the quantile regression coefficients corresponding to the trigonometric regressors.
When facing multivariate covariates, general semiparametric regression techniques come at hand to propose flexible models that are unexposed to the curse of dimensionality. Then the application to analysing quantile and tail area dependence in foreign exchange markets is provided. The consistency of nonlinear quantile regression estimation has been investigated by white 1994, engle and manganelli 2000and kim and white 2002. Pdf a quantile regression approach and nonlinear analysis with. Section 2 introduces the copula quantile regression model. Jun and pinkse 5 and waldmann and kneib 6 extended the sur model of zellner 1 to quantile in feature to gain more robustness against outliers in the response measurements and allow. Propose a kernelbased support vector quantile regression svqr model.
Quantile regression is a basic tool for estimating conditional quantiles of a response variable y given a vector of regressors x. The present paper uses copula quantile on quantile regression cqqr to model correlation structure. Shortterm power load probability density forecasting method using kernelbased support vector quantile regression and copula theory yaoyao hea,b,c. Quantile regression 8 quantile plot this plot shows the fitted regression models for each specified quantile. This article investigates the utility of copula models for model. Shortterm power load probability density forecasting.
Moreover, the vine copula based quantile regression approach is benchmarked against both classical linear quantile regression and expectile regression in order to illustrate its methodological effectiveness in the scenarios evaluated. Bayesian estimation of archimedean copulabased sur quantile. Then the curve y\\tildeyx is the quantile regression curve of v or. A copula is a function which couples a multivariate distribution function to its marginal distribution functions, generally called marginals or simply margins.
An adaptive soft sensor method of dvine copula quantile. Analyze the diagram of power load and realtime price by copula theory. Application of quantile regression to recent genetic and. In 6 solve the problem of modeling extreme data with the gaussian copula marginal regression. Copula quantile regression and measurement of risk in. Jan 01, 2020 quantile regression estimators have the same equivariance property as the ordinary least square ols estimators but the equivariance to monotone transformations is specific only to quantile regression see koenker, 2005 for more details. The linear quantile regression method bykoenker and bassett1978 has been criticized by. Apr 26, 2014 using copula quantile regression, the dependence \\rho\ can be estimated at various quantiles. Quantile regression uses an l1loss function, and the optimal solution of linear programming for estimating coefficients of regression.
248 926 1707 18 574 1008 1551 792 1759 1163 478 730 1449 983 22 139 719 872 1533 128 1110 809 658 44 383 1640 953