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Correcting outliers in GARCH models: a weighted forward approach

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Abstract

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.

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Notes

  1. This point was suggested by a referee.

  2. We are very grateful to a referee who brought our attention to this point.

  3. In all simulations and applications (see Sect. 5) the distribution of the standardized squared residuals used to compute the unit weights has always been the \(\chi ^2_1\) (see Sect. 3.2 for details).

  4. Weekly frequency makes it possible to analyze long time periods with not too long time series. On the other hand, the presence of extreme returns is more probable than in the case of daily returns.

  5. The same plots are available for the remaining companies analyzed and can be obtained from the authors upon request.

Abbreviations

FS:

Forward search

WFS:

Weighted forward search

CDS:

Clean data set

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Acknowledgements

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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Authors and Affiliations

  1. Department of Economics, Management and Statistics (DEMS), University of Milano - Bicocca, via Bicocca degli Arcimboldi 8, 26100, Milan, Italy

    Lisa Crosato

  2. Department of Economics, University of Verona, Via Cantarane, 24, 37129, Verona, Italy

    Luigi Grossi

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  1. Lisa Crosato
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  2. Luigi Grossi
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Correspondence to Luigi Grossi.

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Crosato, L., Grossi, L. Correcting outliers in GARCH models: a weighted forward approach. Stat Papers 60, 1939–1970 (2019). https://doi.org/10.1007/s00362-017-0903-y

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