Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

TL;DR

This paper introduces a practical hybrid quantile regression method for GARCH models in financial time series, providing asymptotic theory, bootstrap inference, and diagnostic tools, with demonstrated effectiveness through simulations and empirical data.

Contribution

It develops a novel hybrid quantile estimation procedure for GARCH models, including asymptotic analysis, bootstrap inference, and diagnostic tools, enhancing quantile regression in heteroscedastic time series.

Findings

The proposed estimator performs well in finite samples.

Bootstrap methods effectively approximate the estimator's distribution.

Diagnostic tools reliably assess model adequacy.

Abstract

Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of conditional heteroscedastic models, the generalized autoregressive conditional heteroscedastic (GARCH) process is the most popular and influential one. So far, feasible quantile regression methods for this task have been confined to a variant of the GARCH model, the linear GARCH model, owing to its tractable conditional quantile structure. This paper considers the widely used GARCH model. An easy-to-implement hybrid conditional quantile estimation procedure is developed based on a simple albeit nontrivial transformation. Asymptotic properties of the proposed estimator and statistics are derived, which facilitate corresponding inferences. To approximate the asymptotic distribution of the quantile regression estimator, we introduce a mixed bootstrapping procedure, where a time-consuming optimization is replaced by a sample averaging. Moreover, diagnostic tools based on the residual quantile autocorrelation function are constructed to check the adequacy of the fitted conditional quantiles. Simulation experiments are carried out to assess the finite-sample performance of the proposed approach. The favorable performance of the conditional quantile estimator and the usefulness of the inference tools are further illustrated by an empirical application.