Bootstrap method for misspecified ergodic Lévy driven stochastic differential equation models

09/11/2020
by   Yuma Uehara, et al.
0

In this paper, we consider possibly misspecified stochastic differential equation models driven by Lévy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, in the misspecified case, the asymptotic distribution of the estimator varies by the correction of the misspecification bias, and consistent estimators for the asymptotic variance proposed in the correctly specified case may lose theoretical validity. As one of its solutions, we propose a bootstrap method for approximating the asymptotic distribution. We show that our bootstrap method theoretically works in both correctly specified case and misspecified case without assuming the precise distribution of the driving noise.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

11/03/2021

Noise Inference For Ergodic Lévy Driven SDE

We study inference for the driving Lévy noise of an ergodic stochastic d...
03/24/2022

Parameter estimation for ergodic linear SDEs from partial and discrete observations

We consider a problem of parameter estimation for the state space model ...
01/02/2022

Parameter estimation of stochastic differential equation driven by small fractional noise

We study the problem of parametric estimation for continuously observed ...
04/28/2019

Schwartz type model selection for ergodic stochastic differential equation models

We study the construction of the theoretical foundation of model compari...
04/02/2021

Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion

The paper deals with projection estimators of the density of the station...
09/17/2019

On Explicit Tamed Milstein-type scheme for Stochastic Differential Equation with Markovian Switching

We propose a new tamed Milstein-type scheme for stochastic differential ...
03/08/2022

Gaussian quasi-information criteria for ergodic Lévy driven SDE

We consider relative model comparison for the parametric coefficients of...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.