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

This paper proposes consistent and asymptotically Gaussian estimators for the parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\lambda , \sigma $$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$H$$</EquationSource> </InlineEquation> of the discretely observed fractional Ornstein–Uhlenbeck process solution of the stochastic differential equation <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$d Y_t=-\lambda Y_t dt + \sigma d W_t^H$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$(W_t^H, t\ge 0)$$</EquationSource> </InlineEquation> is the fractional Brownian motion. For the estimation of the drift <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\lambda $$</EquationSource> </InlineEquation>, the results are obtained only in the case when <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\frac{1}{2} > H > \frac{3}{4}$$</EquationSource> </InlineEquation>. This paper also provides ready-to-use software for the <Emphasis FontCategory="NonProportional">R statistical environment based on the YUIMA package. Copyright Springer-Verlag 2013