Use of tempered stable distributions in $GARCH(1, 1)$ models

Use of classical and modified tempered stable distributions for $GARCH$ models is considered in the paper. Such models are applied for the analysis of financial and economic time series, which have several special properties: volatility clustering, heavy tails and asymmetry of residuals distributions. Comparison of the properties of stable and tempered stable distributions is presented; methodologies for constructing models and subsequent estimation of parameters using the maximum likelihood method are described. An experimental based on model data comparative analysis of the accuracy of models parameters estimates for different residuals distributions was held, and it confirms the operability of the used methods. An example of building models on real data is considered.