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.

本文提出了可在潜在存在加性低频污染的场景下，对平稳遍历短记忆时间序列（stationary ergodic short-memory time series）模型的参数开展稳健估计的方法。所涵盖的污染类型包括水平漂移（均值变动）与单调或平滑时间趋势，已有研究证实，这两类污染会在各类场景下使参数估计结果偏向持续性区域。本文提出的估计量可在无需指定低频污染成分的前提下，最小化截尾频域拟极大似然（frequency domain quasi-maximum likelihood, FDQML）目标函数。当采用合适的依赖样本量的截尾参数时，该FDQML估计量具备相合性与渐近正态性，可渐近消除所有伪持续性的影响。该渐近性质在不存在加性低频污染的场景下同样成立，使得从业者可在无需预先知晓是否存在污染的情况下，稳健估计模型参数。适配本文研究框架的主流时间序列模型包括自回归移动平均（autoregressive moving average, ARMA）模型、随机波动率模型、广义自回归条件异方差（generalized autoregressive conditional heteroscedasticity, GARCH）模型以及自回归条件异方差（autoregressive conditional heteroscedasticity, ARCH）模型。本文探究了上述部分模型参数的截尾FDQML估计量的有限样本性质，并为截尾参数的选择提供了实操指导。实证估计结果显示，部分波动率时间序列中观测到的持续性，很大程度上实为伪持续性。本文配套补充材料可在线获取。