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Inference in (M)GARCH Models in the Presence of Additive Outliers: Specification, Estimation, and Prediction

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Abstract

The (M)GARCH models are probably the most widely used to estimate and predict volatility. Estimation and prediction of volatility are very important in many financial applications. One important issue in the application of (M)GARCH models is the frequent presence of outliers in financial time series and their effects in all stages of model application. We present some issues involved in making inference in (M)GARCH models in the presence of additive outliers. Specifically, we present the effects of outliers on specification, estimation of models, and their volatility and volatility prediction. We also present some robust methods to estimate the model and to predict volatility. We emphasize the presentation of robust methods for volatility forecast density.

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Notes

  1. 1.

    In this chapter we will not present Bayesian methodologies. However, the reader interested can see [51, 58, 89] for some references.

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Acknowledgements

The first author acknowledges financial support from São Paulo Research Foundation (FAPESP), grants 2013/00506-1 and 2013/22930-0. The second author is also grateful for financial support from FAPESP, grants 2012/09596-0 and 2016/18599-4. Both authors acknowledge the support of the Centre of Applied Research on Econometrics, Finance and Statistics (CAREFS).

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  1. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil

    Luiz Koodi Hotta

  2. São Paulo School of Economics, Getúlio Vargas Foundation, São Paulo, SP, Brazil

    Carlos Trucíos

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  1. Luiz Koodi Hotta
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  1. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, São Paulo, Brazil

    Carlile Lavor

  2. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, São Paulo, Brazil

    Francisco A. M. Gomes

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Hotta, L.K., Trucíos, C. (2018). Inference in (M)GARCH Models in the Presence of Additive Outliers: Specification, Estimation, and Prediction. In: Lavor, C., Gomes, F. (eds) Advances in Mathematics and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-94015-1_8

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