Mixed tempered stable distribution

In this paper, we introduce a new parametric distribution, the mixed tempered stable. It has the same structure of the normal variance–mean mixtures but the normality assumption gives way to a semi-heavy tailed distribution. We show that, by choosing appropriately the parameters of the distribution and under the concrete specification of the mixing random variable, it is possible to obtain some well-known distributions as special cases. We employ the mixed tempered stable distribution which has many attractive features for modelling univariate returns. Our results suggest that it is flexible enough to accommodate different density shapes. Furthermore, the analysis applied to statistical time series shows that our approach provides a better fit than competing distributions that are common in the practice of finance.