Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155843 | Stochastic Processes and their Applications | 2012 | 25 Pages |
Abstract
We consider a multidimensional Itô process Y=(Yt)t∈[0,T]Y=(Yt)t∈[0,T] with some unknown drift coefficient process btbt and volatility coefficient σ(Xt,θ)σ(Xt,θ) with covariate process X=(Xt)t∈[0,T]X=(Xt)t∈[0,T], the function σ(x,θ)σ(x,θ) being known up to θ∈Θθ∈Θ. For this model, we consider a change point problem for the parameter θθ in the volatility component. The change is supposed to occur at some point t∗∈(0,T)t∗∈(0,T). Given discrete time observations from the process (X,Y)(X,Y), we propose quasi-maximum likelihood estimation of the change point. We present the rate of convergence of the change point estimator and the limit theorems of the asymptotically mixed type.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Stefano M. Iacus, Nakahiro Yoshida,