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Estimation for the change point of volatility in a stochastic differential equation

Stefano Iacus () and Nakahiro Yoshida

Stochastic Processes and their Applications, 2012, vol. 122, issue 3, 1068-1092

Abstract: We consider a multidimensional Itô process Y=(Yt)t∈[0,T] with some unknown drift coefficient process bt and volatility coefficient σ(Xt,θ) with covariate process X=(Xt)t∈[0,T], the function σ(x,θ) being known up to θ∈Θ. For this model, we consider a change point problem for the parameter θ in the volatility component. The change is supposed to occur at some point t∗∈(0,T). Given discrete time observations from the process (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.

Keywords: Itô processes; Discrete time observations; Change point estimation; Volatility (search for similar items in EconPapers)
Date: 2012
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Working Paper: Estimation for the change point of the volatility in a stochastic differential equation (2009) Downloads
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