Robust Methods of Testing Long Range
This thesis develops a novel robust periodogram method for detecting long memory. Though many test for long memory are based on the idea of linear regression, there exists no results in statistical literature on utilizing the robust regression methodology for detection of long memory. The advantage of the robust regression is a substantially less sensitivity to atypical observations or outliers, compared to the classical regression that is based on the least squares method. The thesis suggests two versions of the robust periodogram methods based on the least quan- tile and the least trimmed methods. The new robust periodogram methods are shown to provide smaller bias in long memory estimation when compared with the classical periodogram method. However, variability of estimation is increased. Therefore, we develop the bootstrapped modification of the new robust periodogram methods to reduce variability of estimation. The new bootstrapped modi¯cations of the robust periodogram tests substantially reduce variance of estimation and provides a competitively low bias. All proposed robust methods are illustrated by simulations and the case studies on currency exchange rates, and comparative analysis with other existing tests for long memory is carried out.