Robust Econometrics

(2001), Zinde-Walsh (2002), and Cizek (2005) for various S-type estimators.
In these cases, the results are usually established for general nonlinear mod-
els.

Second, the effects of data contamination are more complex and wide
spread due to time-dependency: an error in one observation is transferred,
by means of a model, to other ones close in time. The possible effects of
outliers in time series are elaborated by Chen and Liu (1993) and Tsay et al.
(2000), for instance. The first work also offers a sequential identification of
outliers (an alternative procedure based on τ -estimators is offered by Bianco
et al., 2001). Consequently, the robust properties in time series differ from
those experienced in cross-sectional data. For example, the breakdown point
is asymptotically zero in the case of M -estimators (Sakata and White, 1995)
and can be much below 0.5 for various S-estimators (Genton and Lucas,
2003).

A further issue specific to time series is testing for stationarity of a series.
Effects of outliers are in this respect similar to those of neglected struc-
tural changes. To differentiate between random outliers and real structural
changes, robust tests for change-point detection were proposed by Gagliar-
dini et al. (2005), Fiteni (2002), and Fiteni (2004); the last paper uses τ-
estimation. The asymptotics of M -estimators under unit-root assumption
and the corresponding tests were established, for example, by Lucas (1995),
Koenker and Xiao (2004), and Haldrup et al. (2005). An early reference is

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