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

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  • Stefano Maria IACUS
  • Nakahiro YOSHIDA

Abstract

We consider a multidimensional Ito process Y=(Y_t), t in [0,T], with some unknown drift coefficient process b_t and volatility coefficient sigma(X_t,theta) with covariate process X=(X_t), t in[0,T], the function sigma(x,theta) being known up to theta in Theta. For this model we consider a change point problem for the parameter theta in the volatility component. The change is supposed to occur at some point t* in (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 thereoms of aymptotically mixed type.

Suggested Citation

  • Stefano Maria IACUS & Nakahiro YOSHIDA, 2009. "Estimation for the change point of the volatility in a stochastic differential equation," Departmental Working Papers 2009-49, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2009-49
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    References listed on IDEAS

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    Cited by:

    1. Stefano M. Iacus & Nakahiro Yoshida, 2010. "Numerical Analysis of Volatility Change Point Estimators for Discretely Sampled Stochastic Differential Equations," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 107-127, February.

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