Statistical Methods and Applications

, Volume 11, Issue 2, pp 247–264 | Cite as

Analytic Hessian matrices and the computation of FIGARCH estimates

  • Marco J. Lombardi
  • Giampiero M. Gallo
Statistical Applications


Long memory in conditional variance is one of the empirical features exhibited by many financial time series. One class of models that was suggested to capture this behavior is the so-called Fractionally Integrated GARCH (Baillie, Bollerslev and Mikkelsen 1996) in which the ideas of fractional integration originally introduced by Granger (1980) and Hosking (1981) for processes for the mean are applied to a GARCH framework. In this paper we derive analytic expressions for the second-order derivatives of the log-likelihood function of FIGARCH processes with a view to the advantages that can be gained in computational speed and estimation accuracy. The comparison is computationally intensive given the typical sample size of the time series involved and the way the likelihood function is built. An illustration is provided on exchange rate and stock index data.


Conditional Variance GARCH Model Outer Product Financial Time Series Spot Exchange Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2002

Authors and Affiliations

  • Marco J. Lombardi
    • 1
  • Giampiero M. Gallo
    • 1
  1. 1.Dipartimento di Statistica “G. Parenti”Università di FirenzeFirenzeItaly

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