Constrained nonlinear programming for volatility estimation with GARCH models

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Salih A., Pincar M., Leyffer S.

SIAM REVIEW, vol.45, no.3, pp.485-503, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 3
  • Publication Date: 2003
  • Doi Number: 10.1137/s003614450140011
  • Journal Name: SIAM REVIEW
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.485-503
  • Keywords: time series econometrics, constrained nonlinear programming, multivariate CARCH, volatility estimation, maximum likelihood estimation, MULTIVARIATE, EXCHANGE
  • TED University Affiliated: No


This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our results demonstrate that constrained nonlinear programming is a worthwhile exercise for GARCH models, especially for the bivariate and trivariate cases, as they offer a significant improvement in the quality of the solution of the optimization problem over the diagonal VECH and the BEKK representations of the multivariate GARCH model.