Analytic derivatives and the computation of GARCH estimates

Fiorentini, Gabriele; Calzolari, Giorgio; Panattoni, Lorenzo

doi:10.1002/(sici)1099-1255(199607)11:4<399::aid-jae401>3.0.co;2-r

Cited by 107 publications

(88 citation statements)

References 23 publications

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“…EVIEWS, GAUSS, MATLAB, Ox, RATS, S-PLUS, TSP) and there are also a few free open source implementations. [41], [69], and [20] discussed numerical accuracy issues associated with maximizing the GARCH log-likelihood. They found that starting values, optimization algorithm choice, and use of analytic or numerical derivatives, and convergence criteria all influence the resulting numerical estimates of the GARCH parameters.…”

Section: Numerical Accuracy Of Garch Estimatesmentioning

confidence: 99%

Practical Issues in the Analysis of Univariate GARCH Models

Zivot

2009

Handbook of Financial Time Series

128

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Section: Numerical Accuracy Of Garch Estimatesmentioning

confidence: 99%

Practical Issues in the Analysis of Univariate GARCH Models

Zivot

2009

Handbook of Financial Time Series

128

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“…It is possible to formulate recursions for computing the gradient of the likelihood with respect to the static parameters θ. Gradient recursions for the GARCH model have been developed by Fiorentini, Calzolari, and Panattoni (1996). For the GAS(1,1) specification, we obtain…”

Section: Estimation and Inferencementioning

confidence: 99%

A General Framework for Observation Driven Time-Varying Parameter Models

Koopman

Creal

2008

SSRN Journal

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We propose a new class of observation driven time series models referred to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled score of the likelihood function. This approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration, the autoregressive conditional intensity, and the single source of error models. In addition, the GAS specification provides a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions, and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.

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“…3 McCullough and Renfro (1999) proposed the use of the FCP (Gabrielle Fiorentini et al, 1996) GARCH benchmark as a resolution to this problem. Software developers appear to be standardizing their GARCH procedures on this benchmark, as shown by Chris Brooks et al (2001).…”

Section: Maximizing a Likelihoodmentioning

confidence: 99%