Skip to main content
SpringerLink
Log in

Robust estimation of the simplified multivariate GARCH model

  • Published:
Empirical Economics Aims and scope Submit manuscript

Abstract

In this paper, robust M-estimation of multivariate GARCH models are considered. The simplified GARCH model is chosen that involves the estimation of only univariate GARCH models, and hence easy to estimate, and does not put additional constraints on the model. The results of Monte Carlo simulations showed that accurate estimates of conditional correlations can be obtained using these robust estimators when the errors are heavy-tailed. We also investigate the forecasting performance of the class of robust estimators in predicting value-at-risk using various evaluation measures and collect empirical evidences of the better predictive potential of estimators such as LAD and B-estimator over the widely-used quasi-maximum likelihood estimator for the estimation and prediction of multivariate GARCH models. Applications to real data sets are also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Andersen TG, Bollerlsev T (1998) Answering the skeptics: yes, standard volatility models do provide accurate forecasts. Int Econ Rev 39: 885–905

    Article  Google Scholar 

  • Bauwens L, Laurent S, Rombouts JVK (2006) Multivariate GARCH models: a survey. J Appl Econ 21: 79–109

    Article  Google Scholar 

  • Berkes I, Horváth L (2004) The efficiency of the estimators of the parameters in GARCH processes. Ann Stat 32: 633–655

    Article  Google Scholar 

  • Bollerslev T, Engle RF, Wooldridge JM (1988) A capital asset pricing model with time-varying covariances. J Political Econ 96: 116–131

    Article  Google Scholar 

  • Bollerslev T (1990) Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev Econ Stat 72: 498–505

    Article  Google Scholar 

  • Brailsford TJ, Faff RW (1996) An evaluation of volatility forecasting technique. J Bank Financ 20: 419–438

    Article  Google Scholar 

  • Engle RF, Kroner KF (1995) Multivariate simultaneous generalized ARCH. Econom Theory 11: 122–150

    Article  Google Scholar 

  • Engle RF (2002) Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J Bus Econ Stat 20: 339–350

    Article  Google Scholar 

  • Engle RF, Manganelli S (2004) CAViaR: conditional autoregressive value at risk by regression quantiles. J Bus Econ Stat 22: 367–381

    Article  Google Scholar 

  • Glosten L, Jagannathan R, Runkle D (1993) On the relation between the expected value and the volatility on the nominal excess returns on stocks. J Financ 48: 1779–1801

    Article  Google Scholar 

  • Harris RDF, Stoja E, Tucker J (2007) A simplified approach to modelling the comovement of asset returns. J Futur Mark 27: 575–598

    Article  Google Scholar 

  • He C, Teräsvirta T (2004) An extended constant conditional correlation GARCH model and its fourth-moment structure. Econom Theory 20: 904–926

    Article  Google Scholar 

  • Higham N (2002) Computing the nearest correlation matrix—a problem from finance. IMA J Numer Anal 22: 329–343

    Article  Google Scholar 

  • Hosking JRM (1980) The multivariate portmanteau statistics. J Am Stat Assoc 75: 602–608

    Article  Google Scholar 

  • Iqbal F, Mukherjee K (2010) M-estimators of some GARCH-type models: computation and application. Stat Comput 20: 435–445

    Article  Google Scholar 

  • Jeantheau T (1998) Strong consistency of estimators of multivariate ARCH models. Econom Theory 14: 70–86

    Article  Google Scholar 

  • Kupiec PH (1995) Techniques for verifying the accuracy of risk measurement models. J Deriv 3: 73–84

    Article  Google Scholar 

  • Ledoit O, Santa-Clara P, Wolf M (2003) Flexible multivariate GARCH modeling with an application to international stock markets. Rev Econ Stat 85: 735–747

    Article  Google Scholar 

  • Lopez JA (1999) Methods for evaluating Value-at-Risk estimates. Fed Reserv Bank San Francisco Econ Rev:3-17

  • Mukherjee K (2008) M-estimation in GARCH model. Econom Theory 24: 1530–1553

    Article  Google Scholar 

  • Peng L, Yao Q (2003) Least absolute deviations estimation for ARCH and GARCH models. Biom 90: 967–975

    Google Scholar 

  • Skintzi V, Skiadopoulos G, Refenes AP (2005) The effect of mis-estimating correlation on value-at-risk. J Altern Invest 4: 66–82

    Article  Google Scholar 

  • Tsay RS (2010) Analysis of Financial Time Series, 3rd Ed. Wiley, Hoboken

    Book  Google Scholar 

  • Tse YK, Tsui AKC (2002) A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. J Bus Econ Stat 20: 351–362

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Balochistan, Quetta, Pakistan

    Farhat Iqbal

Authors
  1. Farhat Iqbal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farhat Iqbal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iqbal, F. Robust estimation of the simplified multivariate GARCH model. Empir Econ 44, 1353–1372 (2013). https://doi.org/10.1007/s00181-012-0588-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00181-012-0588-y

Keywords

JEL Classification

Search

Navigation