We introduce Ising-Hüsler-Reiss processes, a new class of multivariate Lévy processes that allows for sparse modeling of the path-wise conditional independence structure between marginal stable processes with different stability indices. The underlying conditional independence graph is encoded as zeroes in a suitable precision matrix. An Ising-type parametrization of the weights for each orthant of the Lévy measure allows for data-driven modeling of asymmetry of the jumps while retaining an arbitrary sparse graph. We develop consistent estimators for the graphical structure and asymmetry parameters, relying on a new uniform small-time approximation for Lévy processes. The methodology is illustrated in simulations and a real data application to modeling dependence of stock returns.

翻译：我们引入了Ising-Hüsler-Reiss过程，这是一类新型多元Lévy过程，能够对不同稳定性指数的边缘稳定过程之间的路径条件独立结构进行稀疏建模。其底层条件独立图通过一个适当精度矩阵中的零元素进行编码。通过对Lévy测度每个象限权重的Ising型参数化，可以在保持任意稀疏图结构的同时，实现跳跃不对称性的数据驱动建模。基于Lévy过程的新型均匀短时逼近方法，我们开发了图结构与不对称性参数的一致性估计器。该方法在仿真实验及股票收益依赖关系建模的实际数据应用中得到了验证。