The Sensitivity of Detrended Long-Memory Processes

Abstract

Long-memory tests are often complicated by the presence of deterministic trends. Hence, an additional step of detrending the data is necessary. The typical way to detrend a suspected long-memory series is to use OLS or BSP residuals. Applying the method of sensitivity analysis we address the of question of how robust these residuals are in presence of potential long memory components. Unlike short-memory ARMA process long-memory I(d) processes causes sensitivity to OLS/BSP residuals. Therefore, we develop a finite sample measure of the sensitivity of a detrended series based on the residuals. Based on our sensitivity measure we propose a “rule of thumb” for practitioners to choose between the two methods of detrending, has been provided in this article.

Keywords:

• Detrending
• Long memory
• Sensitivity measure

Mathematics Subject Classification:

• 37M10

Acknowledgment

The author would like to thank ESRC (grant number RES-000-22-0646) and the British Academy for their financial support. I would like to thank the anonymous referee for very useful comments.

Notes

For example, the Geweke and Porter-Hudak (1983) test, the modified rescaled range test of Lo (1991) and Lagrange multiplier (Robinson, 1991, 4). Dolado et al. (2002b) developed a fractional Dickey-Fuller test using an auxiliary nonlinear regression along the lines of Dickey-Fuller test but is inefficient. Recently, Lobato and Velasco (2007) proposed an efficient Wald test for fractional unit root.

Normality is not crucial for the definition.