Title: Local asymptotic normality for discretely observed jump-diffusion processes
Authors: Teppei Ogihara - University of Tokyo (Japan) [presenting]
Yuma Uehara - Kansai University (Japan)
Abstract: When we try to show the local asymptotic normality (LAN) of jump-diffusion processes with discrete observations, there are two problems. The first one is to control transition density ratios between two different values of the parameter. To solve this, we use the scheme with the so-called L2 regularity condition. The original scheme cannot be applied for jump-diffusion processes because of their fat-tailed behaviors. Therefore, we extend the scheme so that it can be applied to jump-diffusion processes. The second problem is that the transition probability for no jump is quite different from that for the presence of jumps. This fact makes it difficult to identify the asymptotic behavior of the likelihood function. To deal with this problem, we approximate the original likelihood function by using a thresholding likelihood function that detects the existence of jumps. As a consequence of these techniques, we obtain LAN for jump-diffusion processes. Moreover, the quasi-maximum-likelihood and Bayes-type estimators are shown to be asymptotically efficient in this model.