Effects of level shifts and temporary changes on the estimation of GARCH models

Abstract

The aim of this article is to analyse the effect of the level shift and temporary change outliers on the estimation of a model with conditional heteroscedasticity, a concept rarely dealt with up to now, the literature focusing more on additive outliers. To do this, we have conducted various Monte Carlo experiments in which the bias produced by these outliers is analysed.

Keywords:

• GARCH models
• level shift
• temporary change
• level outlier
• volatility outlier
• estimation bias

Acknowledgements

This research has been supported by the Spanish Ministry of Science and Technology and FEDER under Project SEC2006-02328 of the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica.

Notes

White and Domowitz 11 establish the theorems necessary to assure the consistency and asymptotic normality of this type of estimator.

There are many works, however, concerning the effects of additive outliers in the context of GARCH models. We can cite, among others, 12–21.

See Trívez and Catalán 22 for an analysis of the specification error caused by this type of outliers.

In the article, we only present the results corresponding to a sample size of 1000. The results for the sample size 200 can be requested from the authors.

Among other authors, we can cite4–6,17 19,23–29. All these authors have used parameters similar to those employed in our research.