Uniform LAN property of locally stable Lévy process observed at high frequency

الأصل · EN

Suppose we have a high-frequency sample from the Lévy process of the form Xₜθ=βt+γZₜ+Uₜ, where Z is a possibly asymmetric locally α-stable Lévy process, and U is a nuisance Lévy process less active than Z. We prove the LAN property about the explicit parameter θ=(β,γ) under very mild conditions without specific form of the Lévy measure of Z, thereby generalizing the LAN result of Aıt-Sahalia and Jacod (2007). In particular, it is clarified that a non-diagonal norming may be necessary in the truly asymmetric case. Due to the special nature of the local α-stable property, the asymptotic Fisher information matrix takes a clean-cut form.