Work

Quasi-likelihood analysis for Student-Lévy regression

Year: 2024

Type: article

Abstract: We consider the quasi-likelihood analysis for a linear regression model driven by a Student-t Lévy process with constant scale and arbitrary degrees of freedom. The model is observed at high frequency over an extending period, under which we can quantify how the sampling frequency affects estimation accuracy. In that setting, joint estimation of trend, scale, and degrees of freedom is a non-trivial problem. The bottleneck is that the Student-t distribution is not closed under convolution, making it difficult to estimate 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. In particular, using full data in the first step causes a problem stemming from the small-time Cauchy approximation, showing the need for data thinning.

Source: Statistical Inference for Stochastic Processes

DOI: 10.1007/s11203-024-09317-2

Authors: Hiroki Masuda, Lorenzo Mercuri, Yuma Uehara

Institutions: The University of Tokyo, University of Milan, Kansai University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: University of Tokyo, Japan Society for the Promotion of Science, Japan Science and Technology Agency, Core Research for Evolutional Science and Technology