Robust Simulation-Based Estimation of ARMA Models
Robust Simulation-Based Estimation of ARMA Models
复制标题
基于鲁棒仿真的 ARMA 模型估计
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Genton
中科院分区：
文献类型：
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作者：
X. de Luna;M. Genton
本文提出了一种新的混合自回归滑动平均(ARMA)模型的稳健估计方法。它是基于最初为具有难以处理的似然函数的模型而提出的间接推理方法。所提出的估计算法基于辅助自回归表示法，其参数首先在观测时间序列上估计，然后根据ARMA模型的模拟数据进行估计。为了模拟数据，必须设置ARMA模型的参数。通过改变这些参数，我们可以最小化基于模拟的辅助估计和基于观测的辅助估计之间的距离。最小收益的自变量则是ARMA模型的参数估计。这种基于模拟的估计过程继承了辅助模型估值器的特性。例如，GM估计器实现了稳健性。与现有的ARMA模型的稳健估计相比，引入的估计量的一个基本特征是它的理论可操作性，这使得我们能够证明相合性和渐近正态。此外，还可以刻画估计量的影响函数和故障点。在一个小样本的蒙特卡罗研究中发现，与现有的方法相比，新的估计器的性能相当好。此外，通过两个实例，我们还比较了提出的推理方法和两种不同的基于孤立点检测的方法。
This article proposes a new approach to the robust estimation of a mixed autoregressive and moving average (ARMA) model. It is based on the indirect inference method that originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed is based on an auxiliary autoregressive representation whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate. The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM estimators. An essential feature of the introduced estimator, compared to existing robust estimators for ARMA models, is its theoretical tractability that allows us to show consistency and asymptotic normality. Moreover, it is possible to characterize the influence function and the breakdown point of the estimator. In a small sample Monte Carlo study it is found that the new estimator performs fairly well when compared with existing procedures. Furthermore, with two real examples, we also compare the proposed inferential method with two different approaches based on outliers detection.