A Semiparametric Approach to Modeling Time-Varying Quantiles

A conditional quantile of a time series can be simply estimated by inverting the (possibly time-varying) conditional distribution. However, it turns out that a parametric assumption about the underlying distribution is felt to be too restrictive. We focus on distribution-free filters for time-varying quantiles. Our approach is motivated by the fact that the first derivatives of the quantile criterion function are, in a sense, similar to conditional score. We propose a Beta-t-IG model for time-varying quantile estimation based of Generalized Autoregressive Score (GAS) framework, also known as Dynamic Conditional Score (DCS) models, allowing parameters to vary over time and capturing the dynamics of time-varying parameters by the autoregressive term and the scaled score of the conditional observation density. We compare our model to the originally proposed specifications of CAViaR models.