  Due to the skessed distribution, high peak and thick tail and asymmetry of
financial return data, it is difficult to describe the traditional
distribution. In recent years, generalized autoregressive score (GAS) has been
used in many fields and achieved good results. In this paper, under the
framework of generalized autoregressive score (GAS), the asymmetric Laplace
distribution (ALD) is improved, and the GAS-ALD model is proposed, which has
the characteristics of time-varying parameters, can describe the peak thick
tail, biased and asymmetric distribution. The model is used to study the
Shanghai index, Shenzhen index and SME board index. It is found that: 1) the
distribution parameters and moments of the three indexes have obvious
time-varying characteristics and aggregation characteristics. 2) Compared with
the commonly used models for calculating VaR and ES, the GAS-ALD model has a
high prediction effect.
