Least‐squares estimation of GARCH(1,1) models with heavy‐tailed errors
提出基于对数变换的最小二乘法估计GARCH(1,1)模型，解决重尾误差下的估计问题，并通过回测和模拟验证了方法的有效性，适用于风险管理和波动率预测。
GARCH(1,1) models are widely used for modelling processes with time‐varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log‐transform‐based least‐squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this difficulty, we propose two alternative two‐stage least‐squares estimators and we derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of n for our estimators. Their finite sample properties are assessed by means of an extensive simulation study.