Local Whittle Analysis of Stationary Fractional Cointegration and the Implied–Realized Volatility Relation
Local Whittle Analysis of Stationary Fractional Cointegration and the Implied–Realized Volatility Relation
复制标题
平稳分数协整的局部削减分析和隐含-已实现波动率关系
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发表时间：
2007
期刊：
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通讯作者：
M. Nielsen
中科院分区：
文献类型：
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作者：
M. Nielsen
我考虑了一个平稳分数次协整模型的局部惠特尔分析。提出了一种局部惠特尔拟极大似然估计，用于联合估计回归变量的积分阶数、误差的积分阶数和协整向量。所提出的估计器是半参数的，因为它使用了对回归量和零频率附近的误差的联合谱密度矩阵的局部假设。证明了估计在弱正则性条件下是相容的，并且在回归和协整误差之间附加局部正交性条件下，我证明了渐近正态。实际上，该估计器对于积分阶数的整个平稳区域是渐近正态的，因此，对于更宽范围的积分阶，它比协整向量的窄带频域最小二乘估计器更好，并且在渐近方差方面优于后者。蒙特卡罗证据证明了新方法的有限样本可行性。在对金融波动率序列的应用中，我检验了隐含-已实现波动率关系中的无偏假设。
I 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 integration 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. I show that the estimator is consistent under weak regularity conditions, and, under an additional local orthogonality condition between the regressors and the cointegration errors, I 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 finite-sample feasibility of the new methodology is presented. In an application to financial volatility series, I examine the unbiasedness hypothesis in the implied–realized volatility relation.