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arXiv · 2111.02049

Noise Inference For Ergodic L\'evy Driven SDE

Hiroki Masuda·Lorenzo Mercuri·Yuma Uehara
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Abstract

We study inference for the driving L\'evy noise of an ergodic stochastic differential equation (SDE) model, when the process is observed at high-frequency and long time and when the drift and scale coefficients contain finite-dimensional unknown parameters. By making use of the Gaussian quasi-likelihood function for the coefficients, we derive a stochastic expansion for functionals of the unit-time residuals, which clarifies some quantitative effect of plugging-in the estimators of the coefficients, thereby enabling us to take several inference procedures for the driving-noise characteristics into account. We also present new classes and methods available in YUIMA for the simulation and the estimation of a L\'evy SDE model. We highlight the flexibility of these new advances in YUIMA using simulated and real data.

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Hiroki Masuda, Lorenzo Mercuri, Yuma Uehara. 2021-11-03. Noise Inference For Ergodic L\'evy Driven SDE. https://arxiv.org/abs/2111.02049

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