Parameter Estimation Robust to Low-Frequency Contamination

28 Pages Posted: 8 Jul 2016

See all articles by Adam McCloskey

Adam McCloskey

University of Colorado at Boulder - Department of Economics

Jonathan B. Hill

University of North Carolina (UNC) at Chapel Hill – Department of Economics

Date Written: July 2015

Abstract

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 towards 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 ARMA, stochastic volatility, GARCH and 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.

Keywords: frequency domain estimation, robust estimation, spurious persistence, level shifts, structural change, deterministic trends, ARMA, stochastic volatility, GARCH

JEL Classification: C13, C22, C51

Suggested Citation

McCloskey, Adam and Hill, Jonathan B., Parameter Estimation Robust to Low-Frequency Contamination (July 2015). Available at SSRN: https://ssrn.com/abstract=2806113 or http://dx.doi.org/10.2139/ssrn.2806113

Adam McCloskey (Contact Author)

University of Colorado at Boulder - Department of Economics ( email )

Economics Building Rm 212 256 UCB
Boulder, CO 80309-0256
United States

Jonathan B. Hill

University of North Carolina (UNC) at Chapel Hill – Department of Economics ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

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