Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

53 Pages Posted: 25 Oct 2016 Last revised: 26 Oct 2016

See all articles by Yao Zheng

Yao Zheng

The University of Hong Kong - Department of Statistics & Actuarial Science

Qianqian Zhu

The University of Hong Kong - Department of Statistics and Actuarial Science

Guodong Li

The University of Hong Kong - Department of Statistics & Actuarial Science

Zhijie Xiao

Boston College - Department of Finance and Department of Economics

Date Written: October 24, 2016

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.

Keywords: Bootstrap Method, Conditional Quantile, GARCH, Nonlinear Time Series, Quantile Regression

JEL Classification: C01

Suggested Citation

Zheng, Yao and Zhu, Qianqian and Li, Guodong and Xiao, Zhijie, Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity (October 24, 2016). Available at SSRN: https://ssrn.com/abstract=2858328 or http://dx.doi.org/10.2139/ssrn.2858328

Yao Zheng (Contact Author)

The University of Hong Kong - Department of Statistics & Actuarial Science ( email )

Pokfulam Road
Hong Kong

Qianqian Zhu

The University of Hong Kong - Department of Statistics and Actuarial Science ( email )

Pokfulam Road
Hong Kong
China

Guodong Li

The University of Hong Kong - Department of Statistics & Actuarial Science ( email )

Hong Kong

Zhijie Xiao

Boston College - Department of Finance and Department of Economics ( email )

United States

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