We consider relative model comparison for the parametric coefficients of a semiparametric ergodic L\'{e}vy driven model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage Gaussian quasi-likelihood function (GQLF) of the Euler-approximation type. For selections of the scale and drift coefficients, we propose explicit Gaussian quasi-AIC (GQAIC) and Gaussian quasi-BIC (GQBIC) statistics through the stepwise inference procedure. In particular, we show that the mixed-rates structure of the joint GQLF, which does not emerge for the case of diffusions, gives rise to the non-standard forms of the regularization terms in the selection of the scale coefficient, quantitatively clarifying the relation between estimation precision and sampling frequency. Numerical experiments are given to illustrate our theoretical findings.

翻译：本文考虑在高频观测下，半参数遍历莱维驱动模型中参数系数的相对模型比较。我们的渐近分析基于欧拉近似类型的完全显式两阶段高斯拟似然函数。针对尺度系数和漂移系数的选择，我们通过逐步推断过程提出了显式的高斯拟AIC和高斯拟BIC统计量。特别地，我们证明联合高斯拟似然函数中混合速率结构（这在扩散情形中不出现）导致了尺度系数选择中正则化项的非标准形式，并定量阐明了估计精度与采样频率之间的关系。数值实验验证了我们的理论发现。