Parameter Estimation Robust to Low-Frequency Contamination

We provide methods to robustly estimate the parameters of stationary ergodic short-memory time series models in the potential presence of additive low-frequency contamination. The types of contamination covered include level shifts (changes in mean) and monotone or smooth time trends, both of which have been shown to bias parameter estimates toward regions of persistence in a variety of contexts. The estimators presented here minimize trimmed frequency domain quasi-maximum likelihood (FDQML) objective functions without requiring specification of the low-frequency contaminating component. When proper sample size-dependent trimmings are used, the FDQML estimators are consistent and asymptotically normal, asymptotically eliminating the presence of any spurious persistence. These asymptotic results also hold in the absence of additive low-frequency contamination, enabling the practitioner to robustly estimate model parameters without prior knowledge of whether contamination is present. Popular time series models that fit into the framework of this article include autoregressive moving average (ARMA), stochastic volatility, generalized autoregressive conditional heteroscedasticity (GARCH), and autoregressive conditional heteroscedasticity (ARCH) models. We explore the finite sample properties of the trimmed FDQML estimators of the parameters of some of these models, providing practical guidance on trimming choice. Empirical estimation results suggest that a large portion of the apparent persistence in certain volatility time series may indeed be spurious. Supplementary materials for this article are available online.

本数据集提供了稳健估计稳态平稳短记忆时间序列模型参数的方法，在可能存在加性低频污染的情况下亦能适用。所涵盖的污染类型包括水平位移（均值变化）以及单调或平滑的时间趋势，这两者在多种情境下均已被证明会偏误参数估计，使其倾向于持久性区域。本文所提出的估计量在无需指定低频污染成分的情况下，最小化了修剪后的频率域准最大似然（FDQML）目标函数。当采用适当的样本量依赖性修剪时，FDQML估计量是一致的，并渐近正态分布，渐近消除了任何虚假持久性的存在。这些渐近结果在不存在加性低频污染的情况下也成立，使得实践者能够在不知污染是否存在的情况下稳健地估计模型参数。符合本文框架的时间序列模型包括自回归移动平均（ARMA）、随机波动率、广义自回归条件异方差（GARCH）和自回归条件异方差（ARCH）模型。我们探讨了这些模型参数的修剪FDQML估计量的有限样本性质，并提供了修剪选择的实用指导。实证估计结果表明，某些波动率时间序列中看似的持久性可能确实为虚假持久性。本文的补充材料可在网上获取。