论文标题
使用耦合对一般本地固定过程的对比估计
Contrast estimation of general locally stationary processes using coupling
论文作者
论文摘要
本文旨在为基于内核的估计时间变化参数提供统计保证，以推动当地固定过程的动态。我们扩展了Dahlhaus等人的结果。 （2018）考虑了Doukhan和Wintenberger（2008）的无限记忆过程的本地固定版本。将估计器计算为任何满足适当收缩条件的对比度的局部M估计器。我们证明了此类基于内核的估计器的统一一致性和渐近正态性。我们将结果应用于通常的对比度，例如最小二乘，绝对价值或准最大可能的可能性对比。还考虑了各种本地阶层的过程，例如ARMA，AR（INFTY），GARCH，ARCH（INFTY），ARMA-GARCH，LARCH（\ infty），...和整数值的过程。数值实验证明了估计器对模拟和真实数据集的效率。
This paper aims at providing statistical guarantees for a kernel based estimation of time varying parameters driving the dynamic of local stationary processes. We extend the results of Dahlhaus et al. (2018) considering the local stationary version of the infinite memory processes of Doukhan and Wintenberger (2008). The estimators are computed as localized M-estimators of any contrast satisfying appropriate contraction conditions. We prove the uniform consistency and pointwise asymptotic normality of such kernel based estimators. We apply our result to usual contrasts such as least-square, least absolute value, or quasi-maximum likelihood contrasts. Various local-stationary processes as ARMA, AR(infty), GARCH, ARCH(infty), ARMA-GARCH, LARCH(\infty),..., and integer valued processes are also considered. Numerical experiments demonstrate the efficiency of the estimators on both simulated and real data sets.
