Specification error caused by level shifts and temporary changes in ARMA–GARCH models

Abstract

The aim of this article is to analyse the effect of the level shifts and temporary changes on the specification of a model with conditional heteroscedasticity, a concept very little 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 effect of these outliers on the principal model identification tools (descriptive statistics, graphs and heteroscedasticity tests) is analysed.

Keywords:

• ARMA–GARCH models
• level shift
• temporary change
• level outlier
• volatility outlier
• lagrange multiplier test
• kurtosis
• asymmetry
• specification error

JEL :

• C22
• C52

Acknowledgements

The authors gratefully acknowledge the helpful observations and suggestions of the anonymous referees. This research has been supported by the Spanish Ministry of Education and Science and FEDER under Project SEJ2006-02328 of the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica.

Notes

^†In the context of the ARIMA models, see Trívez and Nievas 13.

^†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 cite: Franses and Ghijsels 14, Carnero et al. 15, Verhoeven and Mc Aleer 16, Franses and Van Dijk 17, Gregory and Reeves 18, Franses and Van Dijk 19, He and Teräsvirta 20, Hotta and Tsay 21, Park 22, Afonso et al. 11, McCurdy and Morgan 23, Rich et al. 24, Bera et al., 25, Bera and Higgings 26. All these authors have used parameters similar to those employed in our research.