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.

本文提出了在可能存在加性低频污染的情形下，稳健估计平稳遍历短记忆时间序列模型（stationary ergodic short-memory time series models）参数的方法。所涵盖的污染类型包括水平偏移（均值变动）与单调或平滑时间趋势，已有研究证实，在多种应用场景下，这两类污染均会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，最小化修剪频域拟极大似然（trimmed frequency domain quasi-maximum likelihood, FDQML）目标函数。当采用依赖样本量的恰当修剪策略时，该FDQML估计量具备一致性与渐近正态性，可渐近消除任意伪持续性的影响。上述渐近性质在不存在加性低频污染的情形下同样成立，使得研究者无需预先判断是否存在污染，即可稳健估计模型参数。适配本文研究框架的常见时间序列模型包括自回归移动平均（autoregressive moving average, ARMA）、随机波动率（stochastic volatility）、广义自回归条件异方差（generalized autoregressive conditional heteroscedasticity, GARCH）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修剪FDQML估计量的有限样本性质，并就修剪策略的选择提供了实用指导。实证估计结果表明，部分波动率时间序列中观测到的大量表观持续性，实则为伪持续性。本文的补充材料可在线获取。