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英文文献：Adaptive Inference in Heteroskedastic Fractional Time Series Models-异方差分数时间序列模型的自适应推理
英文文献作者：Giuseppe Cavaliere,Morten ?rregaard Nielsen,Robert Taylor
英文文献摘要：
We consider estimation and inference in fractionally integrated time series models driven by shocks which can display conditional and unconditional heteroskedasticity of unknown form. Although the standard conditional sum-of-squares (CSS) estimator remains consistent and asymptotically normal in such cases, unconditional heteroskedasticity inflates its variance matrix by a scalar quantity, \lambda > 1, thereby inducing a loss in efficiency relative to the unconditionally homoskedastic case, \lambda = 1. We propose an adaptive version of the CSS estimator, based on non-parametric kernel-based estimation of the unconditional volatility process. We show that adaptive estimation eliminates the factor \lambda from the variance matrix, thereby delivering the same asymptotic efficiency as that attained by the standard CSS estimator in the unconditionally homoskedastic case and, hence, asymptotic efficiency under Gaussianity. Importantly, the asymptotic analysis is based on a novel proof strategy, which does not require consistent estimation (in the sup norm) of the volatility process. Consequently, we are able to work under a weaker set of assumptions than those employed in the extant literature. The asymptotic variance matrices of both the standard and adaptive CSS estimators depend on any weak parametric autocorrelation present in the fractional model and any conditional heteroskedasticity in the shocks. Consequently, asymptotically pivotal inference can be achieved through the development of confidence regions or hypothesis tests using either heteroskedasticity-robust standard errors and/or a wild bootstrap. Monte Carlo simulations and empirical applications illustrate the practical usefulness of the methods proposed.
摘要研究了由冲击驱动的小积分时间序列模型的估计和推断，该模型能够显示未知形式的条件异方差和无条件异方差。尽管标准条件平方和(CSS)估计量在这种情况下保持一致和渐近正态，无条件异方差将其方差矩阵膨胀为一个标量，\ > 1，从而导致相对于无条件同胚情况的效率损失\ = 1。我们提出了一个自适应版本的CSS估计器，基于非参数的核估计的无条件波动过程。我们证明自适应估计从方差矩阵中消除了因子\lambda，从而在无条件同方差情况下提供了与标准CSS估计器获得的渐近效率相同的渐近效率，因此，在高斯性下渐近效率。重要的是，渐近分析是基于一种新的证明策略，它不需要一致估计(在超范数)的波动过程。因此，我们能够在一套较弱的假设下工作，而不是在现有的文献中使用。标准和自适应CSS估计器的渐近方差矩阵依赖于分式模型中存在的任何弱参数自相关和冲击中的任何条件异方差。因此，可以通过发展置信区域或使用异方差稳健标准误差和/或野bootstrap的假设检验来实现渐近关键推论。蒙特卡罗模拟和经验应用说明了所提方法的实用性。
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