A0526
Title: Quasi-likelihood analysis for Student-Levy regression
Authors: Yuma Uehara - Kansai University (Japan) [presenting]
Lorenzo Mercuri - University of Milan (Italy)
Hiroki Masuda - University of Tokyo (Japan)
Abstract: A linear regression model driven by a Student Levy process with constant scale and arbitrary degrees of freedom is considered. It is supposed that the data is observed at high frequency over a long period. In the proposed model, three estimation targets are considered: trend, scale and the degrees of freedom in the driving noise. However, the distribution of the Student-Levy process at a small time t is not given under closed form, and this makes it difficult to estimate the above three unknown quantities directly from the high-frequency data. Hence the following stepwise estimation procedure is introduced for our model. First, the trend and scale parameter is estimated by Cauchy quasi-likelihood which is based on the fact that the (appropriately scaled) distribution of the Student-Levy process tends to Cauchy distribution as the time tends to 0. After that, the rest parameter by constructing unit-time residual and maximum likelihood estimation is estimated. Also, its asymptotic behaviour, and its simulation aspects are presented.
