Leitura do Dia - cointegração Fracional

Local Whittle Analysis of Stationary Fractional Cointegration
and the Implied-Realized Volatility Relation
Morten Ørregaard Nielseny
Cornell University
March 1, 2006
Abstract. We consider local Whittle analysis of a stationary fractionally
cointegrated model. The local Whittle quasi maximum likelihood estimator is
proposed to jointly estimate the integration orders of the regressors, the integra-
tion order of the errors, and the cointegration vector. The proposed estimator
is semiparametric in the sense that it employs local assumptions on the joint
spectral density matrix of the regressors and the errors near the zero frequency.
We show that the estimator is consistent under weak regularity conditions, and,
under an additional local orthogonality condition between the regressors and the
cointegration errors, we show asymptotic normality. Indeed, the estimator is
asymptotically normal for the entire stationary region of the integration orders,
and thus for a wider range of integration orders than the narrow-band frequency
domain least squares estimator of the cointegration vector, and it is superior to
the latter estimator with respect to asymptotic variance. Monte Carlo evidence
documenting the ...nite sample feasibility of our new methodology is presented.
In an application to ...nancial volatility series, we examine the unbiasedness hy-
pothesis in the implied-realized volatility relation.