Efficient and robust scale estimation for trended time series

Abstract

a b s t r a c tThis paper presents a new method for robust online variability extraction in time series. The proposed estimator is simultaneously highly robust and efficient. We derive its breakdown point, influence function, and asymptotic variance and study the finite sample properties in a simulation study.

On a robust local estimator for the scale function in heteroscedastic nonparametric regression

“…Moreover, as it may be expected, the resistance of the estimators to contamination will decrease as the difference order increases, since contaminations propagate over the considered differences. This fact is analogous to the behavior observed in time series by Caliskan et al (2009) who proposed estimators based on three consecutive observations attaining at most a breakdown point of 0.25, see also Gelper et al (2009). Note also that the breakdown point of the estimators considered in Rousseeuw and Hubert (1996) is at most 20%.…”