Tail dependence, intermediate tail dependence, quantile regression, conditional quan tiles, tawn copula, cauchy copula. Portfolio management and dependencies among precious metal. By use of the copula representation, it turns out to have a remarkable product form. This study examines the dependence structure among four major precious metal markets. Copulabased nonlinear quantile autoregression xiaohong cheny, roger koenker z, and zhijie xiao x october 9, 2008 abstract parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear timeseries. Quantile regression is a basic tool for estimating conditional quantiles of a response variable y given a vector of regressors x. Multisite and multivariable statistical downscaling using. Conditional quantiles and tail dependence pdf university of. This is a pdf file of an unedited manuscript that has been accepted for. We consider a new approach in quantile regression modeling based on the copula function that defines the dependence structure between the variables of interest.
Deep generative quantilecopula models for probabilistic. 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. In such a case, we generally speak about the median regression or the leastabsolutedeviations lad regression ying et al. Dvine copula based quantile regression request pdf. Median regression is more robust to outliers than least squares. Actually, our proposal is an extension of the recent work of noh et al. Then, we introduce the concept of a copula quantile curve, derive some properties of this cquantile curve and provide some examples for particular copulae. Dvine copula based quantile regression and the simplifying.
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. Copula based quantile regression estimates of the onedimensional minimalistic example. A second objective of this paper is to apply the c quantile idea to assess the form and degree. The monte carlo simulations show good results of the proposed weighted method. Then the curve y\tildeyx is the quantile regression curve of v or y. A dvine copulabased quantile regression approach for the prediction of heating energy consumption. If x and y are random variables having quantile functions xf and yg and letting y\tildeyx denote a solution to \mathrmpry. Dynamic copula quantile regressions and tail area dynamic dependence in forex markets. Dvine copula based quantile regression sciencedirect.
Quantile regression, the prediction of conditional quantiles, nds applications in various elds. The dvine copulabased quantile regression model used in this study achieved very good fitting results based on a representative data set comprising 25,000 german households. The resulting quantile regression estimator has the valuable property of being automatically monotonic across quantile levels. The proposed deep quantile copula model suits applications that require accurate and calibrated characterization of each target random variable in multitarget learning, also with the need to simulate or infer the joint distribution of target vector. A quantilecopula approach to conditional density estimation. Quantile regression uses an l1loss function, and the optimal solution of linear programming for estimating coefficients of regression. After the copula and the marginal distributions are estimated, the new. Although quantile regression methods are usually applied to. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. Rochus niemierko masters thesis economics statistics and methods publish your bachelors or masters thesis, dissertation, term paper or essay. Quantile regression analysis has received increasing at tentions in the recent literature of survival analysis. Copulabased quantile autoregression xiaohong chen, roger koenkery, and zhijie xiao z september 4, 2008 abstract parametric copulae are shown to be an attractive device for specifying quantile autoregressive models for nonlinear timeseries.
Using the novel copula quantile on quantile regression cqqr approach of sim 2016, we show that precious metals share a systemic relationship despite their different demandsupply interplays, applications, and the macroeconomic factors, which influence their values. The key idea of this approach is to rewrite the characterization of a regression quantile in terms of a copula and marginal distributions. Applied econometrics boston college, spring 20 christopher f baum bc diw quantile regression boston college, spring 20 1 20. Motivation motivation standard linear regression techniques summarize the average. To this end, the present paper introduces a modular structure combining two statistical tools of increasing interest during the last years. Copula quantile regression and measurement of risk in finance. Specifically, we assume linear quantile regression models for both the event time and the dependent censoring time. Semiparametric copula quantile regression for complete or. We identify vine copula based quantile regression as an eligible tool for conducting such stress tests as this method has good robustness properties, takes into account potential nonlinearities of conditional quantile functions and ensures that no quantile crossing effects occur. We introduce a general approach to nonlinear quantile regression modelling based on the copula function that defines the dependency structure between the variables of interest. Copula quantile regression and measurement of risk in. Nov 19, 2015 to this end, the present paper introduces a modular structure combining two statistical tools of increasing interest during the last years.
The solution of this optimization problem is given by the conditional median. Testing conditional independence via quantile regression. A dvine copula quantile regression approach for the. Dynamic copula quantile regressions and tail area dynamic. This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. A co pulabased quant ileonquantile regression approa ch. Compared with conventional regression models such as the proportional hazards ph model or the accelerated failure time aft model, quantile regression models provide direct assessment of the covariate effect on dif. Quantile regression minimizes a sum that gives asymmetric penalties 1 qjei jfor overprediction and qjei jfor underprediction. The partial copula provides a method for describing the dependence between two random variables x and y conditional on a third random vector z in terms of nonparametric residuals u 1 and u 2.
Then the curve y\tildeyx is the quantile regression curve of v. Perform quantile regression using a copula by numerical derivative method for v with respect to u. On copulabased conditional quantile estimators espace inrs. Pdf recently, two different copulabased approaches have been. Faugeras a quantilecopula approach to conditional density estimation. September 24th, 2002 abstract we introduce a general approach to nonlinear quantile regression modelling that is based on the speci.
Quantile, spatial and logistic regression statistical. Copula based quantile autoregression xiaohong chen, roger koenkery, and zhijie xiao z september 4, 2008 abstract parametric copulae are shown to be an attractive device for specifying quantile autoregressive models for nonlinear timeseries. We refer below to this relationship as a copulaquantile regression cquantile to distinguish it from a quantile regression function which may have been assumed to be linear or estimated nonparametrically, as is common. R code for performing quantile regression using bivariate. 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. We introduce a general approach to nonlinear quantile regression modelling that is based on the specification of the copula function that defines the dependency. Framework gaussian copula marginal regression models di.
Return olatilitvy relationship, quantile regression, copula, copula. We identify vine copula based quantile regression as an eligible tool for conducting such stress tests as this method has good robustness properties, takes into account potential nonlinearities of. Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. Perform quantile regression using a copula by numerical derivative method for v with respect to u perform quantile regression nelsen, 2006, pp. Multisite and multivariable statistical downscaling using a. Shortterm power load probability density forecasting method using kernelbased support vector quantile regression and copula theory yaoyao hea,b,c. Copulabased quantile regression for longitudinal data. This approach obviously relies heavily on the correct speci. Multitask quantile regression under the transnormal model.
Having selected the twoparameter archimedean survival bb8 copula for the leadlagged relationship between silver vix t1 and gold vix t, we now extract copulabased quantile regressions see fig. The authors propose two new quantile regression approaches to handle such mixed discretecontinuous data. This paper proposes a weighted quantile regression method on high quantile regression for certain extreme value sets. 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. Estimation of local, quantilespeci c models o ers some salient advantages over classical. The main purpose of dvine copula based quantile regression is to predict the quantile of a response variable y given the outcome of some predictor variables x 1, x d, d.
This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric. The partial copula provides a method for describing the dependence between two random variables x and y conditional on a third random vector z in terms of nonparametric residuals u1 and u2. The discussion of the properties of the volatility series and empirical ndings in this paper have signi cance for portfolio optimization, hedging strategies, trading strategies and risk management, in general. In this paper we use the archimedean copula nonlinear conditional quantile regression model to. We refer below to this relationship as a copula quantile regression c quantile to distinguish it from a quantile regression function which may have been assumed to be linear or estimated nonparametrically, as is common. Although its computation requires linear programming methods, the quantile regression estimator is asymptotically normally distributed. The major interest is the covariate effects on the quantile of the nonterminal event time. Conditional quantile function, copula, quantile regression. Copulabased quantile regression estimates of the onedimensional minimalistic example. Estimation of local, quantile speci c models o ers some salient advantages over classical. A dvine copulabased quantile regression approach for the. Dependent censoring is handled by assuming that the joint distribution of the two event times follows a parametric copula. Estimation of local, quantilespeci c copulabased time series models o ers some salient. The gaussian, gumbel and frank copulas are used for parametric copula estimation in a, while b depicts the regression.
In the empirical analysis we compare the results from linear quantile regression lqr and copula based nonlinear. The paper proposes a shortterm power load probability density forecasting method using kernelbased support vector quantile regression ksvqr and copula theory. Deep generative quantilecopula 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. Quantile regression in regional frequency analysis. Peng and fine 2009 proposed a quantile regression method for competing risks data based on the cumulative incidence function, which cannot be applied to draw inference on net quantities as desired in the wasid study. Gaussian copula regression using r guido masarotto cristiano varin university of padua ca foscari university, venice 1 21. Multitask quantile regression under the transnormal model jianqing fan, lingzhou xue and hui zou princeton university, pennsylvania state university and university of minnesota abstract we consider estimating multitask quantile regression under the transnormal model, with focus on highdimensional setting. Both of them generalize the continuous dvine quantile regression, where the dependence be. A second objective of this paper is to apply the cquantile idea to assess the form and degree.
Shortterm power load probability density forecasting method. Quantile regression based on semicompeting risks data. We propose a new semiparametric approach that uses copula to. Take the partial derivative of the copula function cu, v with respect to u, where u and v are both defined in 0, 1.
The quantile regression tool is employed to specify the entire conditional distribution of downscaled variables and to address the limitations of traditional. We study its asymptotic properties and compare its bias and variance to competitors based on nonparametric regression. Semiparametric conditional quantile estimation through. It can be used to measure the effect of regressors not only in the center of a distribution, but also in the upper and lower tails. We assume the typical quantile regression normalization under the implicit assumption that the regression function g contains an intercept2. This kind of regression is more robust to outliers and nonnormal errors than the ols 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. The findings suggest that quantile regression increases transparency by.
Oct 18, 2016 r code for performing quantile regression using bivariate copulas 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. Additionally, the copulabased approach allows the analyst to spontaneously take account of common regression concerns such as interactions between covariates or possible transformations of the latter. Shortterm power load probability density forecasting. Predictive assessment of copula models wiley online library. Estimation of local, quantile speci c copula based time series models o ers some salient. Inference and prediction in quantile regression for longitudinal data are challenging without parametric distributional assumptions. 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.
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