Adaptive Random Bandwidth for Inference in CAViaR Models

TL;DR

This paper introduces an adaptive random bandwidth method to improve inference accuracy in CAViaR models by better estimating their time-varying conditional densities, addressing limitations of existing density estimation techniques.

Contribution

The paper develops a novel adaptive random bandwidth approach that robustly estimates time-varying densities for CAViaR models, enhancing inference accuracy without needing bandwidth selection.

Findings

Improved size performance of Wald tests in CAViaR models.

Adaptive random bandwidth effectively captures time-varying densities.

Method extends easily to multivariate quantile regressions.

Abstract

This paper investigates the size performance of Wald tests for CAViaR models (Engle and Manganelli, 2004). We find that the usual estimation strategy on test statistics yields inaccuracies. Indeed, we show that existing density estimation methods cannot adapt to the time-variation in the conditional probability densities of CAViaR models. Consequently, we develop a method called adaptive random bandwidth which can approximate time-varying conditional probability densities robustly for inference testing on CAViaR models based on the asymptotic normality of the model parameter estimator. This proposed method also avoids the problem of choosing an optimal bandwidth in estimating probability densities, and can be extended to multivariate quantile regressions straightforward.