  In this paper we propose a new method for the estimation of a semiparametric
tempered stable L\'{e}vy model. The estimation procedure combines iteratively
an approximate semiparametric method of moment estimator, Truncated Realized
Quadratic Variations (TRQV), and a newly found small-time high-order
approximation for the optimal threshold of the TRQV of tempered stable
processes. The method is tested via simulations to estimate the volatility and
the Blumenthal-Getoor index of the generalized CGMY model as well as the
integrated volatility of a Heston type model with CGMY jumps. The method
outperforms other efficient alternatives proposed in the literature.
