Weighted composite quantile regression estimation of DTARCH models

In modelling volatility in financial time series, the double-threshold autoregressive conditional heteroscedastic (DTARCH) model has been demonstrated as a useful variant of the autoregressive conditional heteroscedastic (ARCH) models. In this paper, we propose a weighted composite quantile regression method for simultaneously estimating the autoregressive parameters and the ARCH parameters in the DTARCH model. This method involves a sequence of weights and takes a data-driven weighting scheme to maximize the asymptotic efficiency of the estimators. Under regularity conditions, we establish asymptotic distributions of the proposed estimators for a variety of heavy- or light-tailed error distributions. Simulations are conducted to compare the performance of different estimators, and the proposed approach is used to analyse the daily S&P 500 Composite index, both of which endorse our theoretical results.