Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package

Alexandre Brouste () and Stefano Iacus ()

Computational Statistics, 2013, vol. 28, issue 4, 1529-1547

Abstract: This paper proposes consistent and asymptotically Gaussian estimators for the parameters $$\lambda , \sigma $$ and $$H$$ of the discretely observed fractional Ornstein–Uhlenbeck process solution of the stochastic differential equation $$d Y_t=-\lambda Y_t dt + \sigma d W_t^H$$ , where $$(W_t^H, t\ge 0)$$ is the fractional Brownian motion. For the estimation of the drift $$\lambda $$ , the results are obtained only in the case when $$\frac{1}{2} > H > \frac{3}{4}$$ . This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package. Copyright Springer-Verlag 2013

Date: 2013
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DOI: 10.1007/s00180-012-0365-6

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