Quantile regression

About: Quantile regression is a research topic. Over the lifetime, 6854 publications have been published within this topic receiving 137646 citations. The topic is also known as: quantile regression.

CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles *

Abstract: Value at Risk (VaR) has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. VaR is defined as the value that a portfolio will lose with a given probability, over a certain time horizon (usually one or ten days). Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Autoregressive Value-at-Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by Koenker and Bassett to determine the unknown parameters. Since the objective function is not differentiable, we use a differential evolutionary genetic algorithm for the numerical optimization. Utilizing the criterion that each period the probability of exceeding the VaR must be independent of all the past information, we introduce a new test of model adequacy, the Dynamic Quantile test. Applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments.

A gentle introduction to quantile regression for ecologists

Abstract: Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variables associated with those processes. As a consequence, there may be a weak or no predictive relationship between the mean of the response variable (y) distribution and the measured predictive factors (X). Yet there may be stronger, useful predictive relationships with other parts of the response variable distribution. This primer relates quantile regression estimates to prediction intervals in parametric error distribution regression models (eg least squares), and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of the estimates for homogeneous and heterogen...

Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research

Abstract: This paper provides a guideline for the practical use of the semi-parametric technique of quantile regression, concentrating on cross-section applications. It summarizes the most important issues in quantile regression applications and fills some gaps in the literature. The paper (a) presents several alternative estimators for the covariance matrix of the quantile regression estimates; (b) reviews the results for a sequence of quantile regression estimates; and (c) discusses testing procedures for homoskedasticity and symmetry of the error distribution. The various results in the literature are incorporated into the generalized method of moments frame-work. The paper also provides an empirical example using data from the Current Population Survey, raising several important issues relevant to empirical applications of quantile regression. The paper concludes with an extension to the censored quantile regression model.