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.