Parameter Estimation for Tempered Stable Distributions Using Cumulant Matching

This paper presents a novel parameter estimation method for tempered stable distributions based on cumulant matching. Estimation techniques, such as Maximum Likelihood Estimation (MLE), face significant challenges due to the intractable density functions of tempered stable distributions. To address this issue, we introduce the Method of Cumulants (MoC), which leverages the analytically simpler cumulants of these distributions for parameter estimation. We derive explicit formulas for the cumulants of classical tempered stable distributions and establish the statistical consistency of the MoC estimator. Through extensive simulations, we demonstrate the efficiency and accuracy of our method, with results indicating low mean squared errors across various parameter settings. This approach not only enhances the theoretical framework for parameter estimation in tempered stable distributions but also shows promising practical applications, particularly in finance. Future work will explore its applicability to other types of tempered stable distributions.