Self-weighted quantile estimation of autoregressive conditional duration model

An efficient market is often related to the market liquidity in a certain sense. In this paper, the autoregressive conditional duration (ACD) model is used for modeling and analyzing the market liquidity based on high-frequency financial data, which takes the volume duration as its measure index. Considering the high peak and heavy tail of high-frequency financial data, the self-weighted quantile regression (SQR) estimators for the unknown parameters in ACD model are constructed. The consistency and asymptotic properties of the estimators are proved. Furthermore, Monte Carlo simulation shows that the SQR estimators with data-driven weights are more accurate than those by traditional quantile regression (QR). Moreover, the performance of SQR estimation performs better with the increase of the proportion of outliers. The mean deviation and mean square error are reduced up to 96.24% and 91.83%, respectively. Finally, we illustrate the SQR method by an empirical analysis of the volume duration for Industrial And Commercial Bank Of China (ICBC) and PingAn Bank stocks in China. Through the Akaike Information Criterion (AIC) and other evaluation criteria, the SQR estimators at different quantiles all possess better performance.