The asymptotic convexity of the negative likelihood function of GARCH models

W. Ip, H. Wong, J. Pan, D.F. Li

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove the convexity of the negative likelihood function in the asymptotic sense for GARCH models. This property provides assurance for the convergence of numerical optimization algorithms for maximum likelihood estimation of GARCH. A simulation study is conducted in order to compare the performance of several different iteration algorithms. An example based on the log-returns of foreign exchange rates is also given.
Original languageEnglish
Pages (from-to)311-331
Number of pages20
JournalComputational Statistics and Data Analysis
Volume50
Issue number2
DOIs
Publication statusPublished - 2006

Keywords

  • GARCH
  • convexity
  • maximum likelihood estimation
  • iterative algorithm
  • convergence
  • foreign exchange rates
  • statistics
  • data analysis

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