Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends
40 Pages Posted: 6 Nov 2012
Date Written: July 30, 2012
Abstract
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 deterministic 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. We also show that a previously developed trimmed local Whittle estimator is robust to the same forms of data contamination. Regardless of whether the underlying long/shortmemory process is contaminated by level shifts or deterministic trends, the estimators are consistent and asymptotically normal with the same limiting variance as their standard untrimmed counterparts. Simulations show that the trimmed estimators perform their intended purpose quite well, substantially decreasing both finite sample bias and root mean-squared error in the presence of these contaminating components. Furthermore, we assess the tradeoffs 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 finite sample biases involved in estimating the memory parameter, we recommend a particular adaptive version of the trimmed log-periodogram estimator that performs well in a wide variety of circumstances. We apply the estimators to stock market volatility data to find that various time series typically thought to be long-memory processes actually appear to be short or very weak long-memory processes contaminated by level shifts or deterministic trends.
Keywords: long-memory processes, semiparametric estimators, level shifts, structural
JEL Classification: C22, C13, C14
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Modeling and Forecasting Realized Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
Modeling and Forecasting Realized Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Realized Exchange Rate Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Exchange Rate Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Exchange Rate Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
The Distribution of Stock Return Volatility
By Torben G. Andersen, Tim Bollerslev, ...
-
By Torben G. Andersen, Tim Bollerslev, ...
-
Range-Based Estimation of Stochastic Volatility Models
By Sassan Alizadeh, Michael W. Brandt, ...
-
By Torben G. Andersen, Tim Bollerslev, ...
-
By Torben G. Andersen, Tim Bollerslev, ...