Two-step estimation of ergodic Lévy driven SDE
Tóm tắt
We consider high frequency samples from ergodic Lévy driven stochastic differential equation with drift coefficient
$$a(x,\alpha )$$
and scale coefficient
$$c(x,\gamma )$$
involving unknown parameters
$$\alpha $$
and
$$\gamma $$
. We suppose that the Lévy measure
$$\nu _{0}$$
, has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of
$$\alpha $$
,
$$\gamma $$
and a class of functional parameter
$$\int \varphi (z)\nu _0(dz)$$
, which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of
$$(\alpha ,\gamma )$$
; and then, for estimating
$$\int \varphi (z)\nu _0(dz)$$
we make use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator.
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