Abstract
This work analyses the impact of additive level outliers in multivariate time series. Our proposal is to extend the procedure by Grané and Veiga (Comput Stat Data Anal 54:2580–2593, 2010) to the context of Multivariate GARCH models by considering random-projections of multivariate residuals. The effectiveness of this new procedure is evaluated through an intensive Monte Carlo study.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We refer to the concept of ALO that appears in [14].
- 2.
Parameters used are: \(\{\mathbf{C} = (0.053, 0.042, 0.020),\mathbf{A} = (0.161, 0.164),\mathbf{B} = (0.983, 0.981)\}\) for the D-BEKK; \(\{\boldsymbol{\alpha }_{0} = (0.010, 0.013),\boldsymbol{\alpha }_{1} = (0.049, 0.067),\boldsymbol{\beta }_{1} = (0.940, 0.926),\boldsymbol{\rho } = (1,-0.606)\}\) for the CCC and \(\{\boldsymbol{\alpha }_{0} = (0.010, 0.013),\boldsymbol{\alpha }_{1} = (0.049, 0.067),\boldsymbol{\beta }_{1} = (0.940, 0.926),\alpha = 0.015,\beta = 0.981\}\) for the DCC, which were chosen by fitting the models to real time series of financial returns.
- 3.
Other percentiles can be used leading to more conservative results.
References
Bauwens, L., Laurent, S., Rombout, J.: Multivariate GARCH models: a survey. J. Appl. Econom. 21, 79–109 (2006)
Bollerslev, T.: Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev. Econ. Stat. 42, 498–505 (1990)
Boudt, K., Daníelsson, J., Laurent, S.: Robust forecasting of dynamic conditional correlation GARCH models. Int. J. Forecasting 29, 244–257 (2013)
Carnero, M., Peña, D., Ruiz, E.: Effects of outliers on the identification and estimation of GARCH models. J. Time Ser. Anal. 28, 471–497 (2007)
Chen, C., Liu, L.: Joint estimation of model parameters and outlier effects. J. Am. Stat. Assoc. 88, 284–297 (1993)
Cuesta-Albertos, J., Fraiman, R., Ransford, T.: Random projections and goodness-of-fit tests in infinite-dimensional spaces. Bull. Braz. Math. Soc. 37, 1–25 (2006)
Cuesta-Albertos, J., del Barrio, E., Fraiman, R., Matrán, C.: The random projection method in goodness of fit for functional data. Comput. Stat. Data Anal. 51, 4814–4831 (2007)
Engle, R.: Dynamic conditional correlation—a simple class of multivariate GARCH models. J. Bus. Econ. Stat. 20, 339–350 (2002)
Engle, R., Kroner, K.: Multivariate simultaneous generalized ARCH. Econom. Theory 11, 122–150 (1995)
Fox, A.: Outliers in time series. J. R. Stat. Soc. B 34, 350–363 (1972)
Franses, P., Ghijsels, H.: Additive outliers, GARCH and forecasting volatility. Int. J. Forecasting 15, 1–9 (1999)
Grané, A., Veiga, H.: Wavelet-based detection of outliers in financial time series. Comput. Stat. Data Anal. 54, 2580–2593 (2010)
Grossi, L., Laurini, F.: A robust forward weighted lagrange multiplier test for conditional heteroscedasticity. Comput. Stat. Data Anal. 53, 2251–2263 (2009)
Hotta, L., Tsay, R.: Outliers in GARCH processes. Manuscript. Graduate School of Business, University of Chicago (1998)
Ledolter, J.: The effect of additive outliers on the forecasts from ARIMA models. Int. J. Forecasting 5, 231–240 (1989)
Roy, S.: On a Heuristic Method of Test Construction and its use in multivariate analysis. Ann. Math. Stat. 24, 220–238 (1953)
Silvennoinen, A., Teräsvirta, T.: Multivariate GARCH models. In: Handbook of Financial Time Series, pp. 201–226. Springer, Berlin (2009)
Van Dijk, D., Franses, P., Lucas, A.: Testing for ARCH in the presence of additive outliers. J. Appl. Econom.14, 539–562 (1999)
Verhoeven, P., McAleer, M.: Modelling outliers and extreme observations for ARMA-GARCH processes. Working Paper, University of Western Australia (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this paper
Cite this paper
Grané, A., Veiga, H., Martín-Barragán, B. (2014). Additive Level Outliers in Multivariate GARCH Models. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_24
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2104-1_24
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2103-4
Online ISBN: 978-1-4939-2104-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)