Title: Quasi-likelihood inference for Student-Levy regression
Authors: Hiroki Masuda - Kyushu University (Japan) [presenting]
Yuma Uehara - Kansai University (Japan)
Abstract: The quasi-likelihood analysis is considered for a linear regression model driven by a Student Levy process with constant scale and arbitrary degrees of freedom. The model is observed at a high frequency over an extended period, which quantitatively clarifies how the sampling frequency affects estimation accuracy. In that setting, however, joint estimation of trend, scale, and degrees of freedom does not seem to have been investigated as yet. The bottleneck is that the Student distribution is not closed under convolution, preventing us from estimating all the parameters fully based on the high-frequency time scale. To efficiently deal with the intricate nature from both theoretical and computational points of view, we propose a two-step quasi-likelihood analysis: first, we make use of the Cauchy quasi-likelihood for estimating the regression-coefficient vector and the scale parameter; then, we construct the sequence of the unit-period cumulative residuals to estimate the remaining degrees of freedom.