Gaussian quasi-information criteria for ergodic Lévy driven SDE

by   Shoichi Eguchi, et al.

We consider relative model comparison for the parametric coefficients of a semiparametric ergodic Lévy driven model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage Gaussian quasi-likelihood function (GQLF) of the Euler-approximation type. For selections of the scale and drift coefficients, we propose explicit Gaussian quasi-AIC (GQAIC) and Gaussian quasi-BIC (GQBIC) statistics through the stepwise inference procedure. In particular, we show that the mixed-rates structure of the joint GQLF, which does not emerge for the case of diffusions, gives rise to the non-standard forms of the regularization terms in the selection of the scale coefficient, quantitatively clarifying the relation between estimation precision and sampling frequency. Numerical experiments are given to illustrate our theoretical findings.


page 1

page 2

page 3

page 4


Data driven time scale in Gaussian quasi-likelihood inference

We study parametric estimation of ergodic diffusions observed at high fr...

A Quasi-Bayesian Perspective to Online Clustering

When faced with high frequency streams of data, clustering raises theore...

Noise Inference For Ergodic Lévy Driven SDE

We study inference for the driving Lévy noise of an ergodic stochastic d...

Quasi-Likelihood Analysis of Fractional Brownian Motion with Constant Drift under High-Frequency Observations

Consider an estimation of the Hurst parameter H∈(0,1) and the volatility...

Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function

In this paper we consider an ergodic diffusion process with jumps whose ...

Non-standard inference for augmented double autoregressive models with null volatility coefficients

This paper considers an augmented double autoregressive (DAR) model, whi...

Partial quasi likelihood analysis

The quasi likelihood analysis is generalized to the partial quasi likeli...