Statistical Papers

, Volume 60, Issue 6, pp 1939–1970 | Cite as

Correcting outliers in GARCH models: a weighted forward approach

  • Lisa Crosato
  • Luigi GrossiEmail author
Regular Article


In this paper we develop a weighted forward search (WFS) approach to the correction of outliers in GARCH(1,1) models relying on the foward search (FS) method introduced by Atkinson and Riani (Robust diagnostic regression analysis. Springer, New York, 2000). The WFS is based on a weighting system of each unit and is an extension of the FS from independent to dependent observations. We propose a WFS test for the detection of outliers in GARCH(1,1) models and a WFS estimator of GARCH(1,1) coefficients which automatically corrects outliers. Extensive Monte Carlo simulations show the good performance of the WFS test with respect to other methods of outlier detection for the same models. The marked similarity between the distribution of MLE before strong contamination of the time series and after decontamination through the WFS proves the reliability of the WFS estimator. Finally, the application of the WFS procedure to several financial time series of the NYSE reveals the effectiveness of the method when extreme returns are observed.


Extreme observations GARCH models Outliers Robust statistics Weighted forward search 



Forward search


Weighted forward search


Clean data set

JEL Classification

C13 C15 C58 C63 



The authors are grateful to two anonymous referees and the Editor who gave valuable suggestions to improve the paper. They also wish to thank all the participants at the final conference of Project MIUR (2012) in Benevento, at Sco Meeting (2013) in Milan, and at the meeting on Robust Statistics at the Joint Research Centre of the European Commission in Ispra (2014) where preliminary versions of the present work were presented. All comments and suggestions have been considered and have contributed to improve the quality of the manuscript. We thank Matteo M. Pelagatti for the use of his R-codes for GARCH estimation. This work was supported by the project MIUR 2012-MISURA and by the Department of Economics (University of Verona), Grant FAR/2015. The usual disclaimer applies.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Economics, Management and Statistics (DEMS)University of Milano - BicoccaMilanItaly
  2. 2.Department of EconomicsUniversity of VeronaVeronaItaly

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