Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends

We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts and de- terministic time trends. The estimators are simple trimmed versions of the popular log-periodogram regression estimator that employ certain sample size-dependent, and in some cases, data-dependent trimmings which discard low-frequency components. Regardless of whether the underlying long/short-memory process is contaminated by level shifts or deterministic trends, our estimators are shown to be consistent and asymptotically normal with the same limiting variance as the standard log-periodogram estimator. An extensive simulation study shows that our estimators perform their in- tended purpose quite well, substantially decreasing both nite sample bias and root mean-squared error in the presence of these contaminating components. Furthermore, we assess the tradeo s involved with their use when such components are not present but the underlying process exhibits strong short-memory dynamics or is contaminated by noise. To balance the potential nite sample biases involved in estimating the mem- ory parameter, we recommend a particular version of our estimators that performs well in a wide variety of circumstances. Finally, we apply our estimators to stock market volatility and hydrological data to nd that many of the time series typically thought to be long-memory processes actually appear to be short-memory processes contaminated by level shifts or deterministic trends.